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Basic subset of a topological space
and mathematical analysis, an open set is a generalization of an open interval in the real line. In a metric space (a set with a distance defined between
Open_set
{\displaystyle S} of a topological space X {\displaystyle X} is called a regular open set if it is equal to the interior of its closure; expressed symbolically
Regular_open_set
Property of topological space
topological space X is called a regular space if every closed set C of X and a point p not contained in C have non-overlapping open neighborhoods. Thus p and
Regular_space
Mathematical measure for topological spaces
mathematics, a regular measure on a topological space is a measure for which every measurable set can be approximated from above by open measurable sets and from
Regular_measure
open sets in X are open, or equivalently, if arbitrary unions of closed sets are closed, or, again equivalently, if the open sets are the upper sets of
Glossary_of_general_topology
Sequence of characters that forms a search pattern
Interface (POSIX) Base Specifications, Issue 7 Regular Expressions, IEEE Std 1003.1-2024, Open Group Open source list of regular expression resources
Regular_expression
Topics referred to by the same term
successive open strings Regular character, a main character who appears more frequently and/or prominently than a recurring character Regular division of
Regular
Functions that send open (resp. closed) subsets to open (resp. closed) subsets
more specifically in topology, an open map is a function between two topological spaces that maps open sets to open sets. That is, a function f : X → Y {\displaystyle
Open_and_closed_maps
American animated sitcom
Quintel attended many open shows at CalArts, an eight-hour festival of student animation. The style and sensibility of Regular Show was difficult to work
Regular_Show
Axioms in topology defining notions of "separation"
the regular open sets form a base for the open sets of X. Any regular space must also be semiregular. X is quasi-regular if for any nonempty open set G
Separation_axiom
Golf tournament held in the United States
courses, the U.S. Open is set up so that scoring is very difficult, with a premium placed on accurate driving. As of 2026, the U.S. Open awards a $22.5 million
U.S._Open_(golf)
Type of mathematical measure
Borel sets of a Hausdorff topological space X that is finite on all compact sets, outer regular on all Borel sets, and inner regular on open sets. These
Radon_measure
Comprehensive list of Magic: The Gathering card sets since its inception in 1993
June 1996, expansion sets were released in a regular pattern: the base sets were released in October with the small expansion sets being released in February
List of Magic: The Gathering sets
List_of_Magic:_The_Gathering_sets
Set of alternative guitar tunings
regular tunings have equal musical intervals between the paired notes of their successive open strings. Guitar tunings assign pitches to the open strings
Regular_tuning
topological space whose regular open sets (sets that equal the interiors of their closures) form a base for the topology. Every regular space is semiregular
Semiregular_space
set Open set Clopen set Fσ set Gδ set Compact set Relatively compact set Regular open set, regular closed set Connected set Perfect set Meagre set Nowhere
List_of_types_of_sets
to "A Regular Epic Final Battle", Mordecai quits The Park, parts ways with Rigby, moves to New York City, and returns to making art. He opens a successful
List of Regular Show characters
List_of_Regular_Show_characters
Boolean algebra with all operators and laws forming a complete logical system
is complete. The algebra of subsets of a given set is a complete Boolean algebra. The regular open sets of any topological space form a complete Boolean
Complete_Boolean_algebra
Roman Catholic priests living in community under a religious rule
The Canons Regular are Catholic priests and religious brothers (canons) who live in community under a rule (Latin: regula and κανών, kanon, in Greek)
Canon_regular
Type of topological space
space is a topological space in which any two disjoint closed sets have disjoint open neighborhoods. Such spaces need not be Hausdorff in general. A
Normal_space
Mathematical approach
T {\displaystyle T} , we can also consider the collection of its regular open sets. This is a frame using as join the interior of the closure of the
Pointless_topology
Set theory concept
constructed as the algebra of regular open sets in the topological space of P (with underlying set P, and a base given by the sets Up of elements q with q≤p)
Boolean-valued_model
Fractal sets in complex dynamics of mathematics
behavior of the function on the Fatou set is "regular", while on the Julia set its behavior is "chaotic". The Julia set of a function f is commonly denoted
Julia_set
American soccer referee (born 1986)
Major League Soccer, where in 2020 she became the first woman to referee a regular season match in 20 years. Penso was the referee for the 2023 FIFA Women's
Tori_Penso
associates to each open set U the ring of all rational functions on that open set; in other words, KX(U) is the set of fractions of regular functions on U
Function field (scheme theory)
Function_field_(scheme_theory)
right-narrow A partially ordered set, (α,≤) in which for all b in α, {c:c∈α∧b≤c} (the up-set of b) is a set. RO The regular open sets of a topological space or
Glossary_of_set_theory
Particular size, weight and style of a typeface
the set of fonts that share an overall design. For instance, the typeface Bauer Bodoni (shown in the figure) includes fonts "Roman 12pt" (or "regular")
Font
Free licensed works in any field
content in regular use. Legally, however, free content is very similar to open content. An analogy is a use of the rival terms free software and open-source
Free_content
Type of cardinal number in mathematics
In set theory, a regular cardinal is a cardinal number that is equal to its own cofinality. More explicitly, this means that κ {\displaystyle \kappa }
Regular_cardinal
topology) are precisely the Lebesgue-measurable sets; and the complete Boolean algebra of regular open sets of R d {\displaystyle \mathbb {R} _{\mathrm {d}
Density_topology
Points with no three in a line
refers to it as "perhaps, my favorite open problem" and gives a simplified proof of the exponential bound on cap sets, namely that for any prime power p
Cap_set
cohomology set H 1 ( F , G ) {\displaystyle H^{1}(F,G)} is zero. Serre's positivity conjecture that if R {\displaystyle R} is a commutative regular local ring
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
US body that sets national monetary policy
national monetary policy. The committee sets monetary policy by specifying the short-term objective for the Fed's open market operations, which is usually
Federal_Open_Market_Committee
Self-contained underwater breathing apparatus
of a rebreather dive is longer than an open-circuit dive, for similar weight and bulk of the set, if the set is bigger than the practical lower limit
Scuba_set
Tennis tournament
The Halle Open known as the Terra Wortmann Open (for sponsorship reasons) is an ATP Tour tennis tournament held in Halle, North Rhine-Westphalia, Germany
Halle_Open
Beyond Euclidean space, there is an infinite set of regular hyperbolic tilings. The five convex regular polyhedra are called the Platonic solids. The
List_of_regular_polytopes
Standard system of axiomatic set theory
In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in
Zermelo–Fraenkel_set_theory
Software library for interpreting regular expressions
Perl Compatible Regular Expressions (PCRE) is a library written in C, which implements a regular expression engine, inspired by the capabilities of the
Perl Compatible Regular Expressions
Perl_Compatible_Regular_Expressions
Occult religious organization founded in 1975
The Temple of Set (ToS) is an occult religious organization founded in 1975. A new religious movement and form of Western esotericism, the Temple espouses
Temple_of_Set
Tennis tournament
The Lexus Eastbourne Open (formerly Rothesay International Eastbourne) is a tennis tournament held at the Devonshire Park Lawn Tennis Club, Eastbourne
Eastbourne_International
Space with topology generated by convex sets
a convex set C {\displaystyle C} is non-empty then C {\displaystyle C} is a closed (respectively, open) set if and only if it is a regular closed (respectively
Locally convex topological vector space
Locally_convex_topological_vector_space
guitar tunings. In particular, this list contains more examples of open and regular tunings, which are discussed in the article on guitar tunings. In addition
List_of_guitar_tunings
collapsing algebras. If κ and λ are cardinals, then the Boolean algebra of regular open sets of the product space κλ is a collapsing algebra. Here κ and λ are
Collapsing_algebra
partial derivatives not vanishing. More precisely, the set I ( n , k ) {\displaystyle I(n,k)} of regular homotopy classes of embeddings of sphere S k {\displaystyle
Regular_homotopy
Stadium in Foxborough, Massachusetts
MBTA Commuter Rail service from Boston and Providence during events, plus regular weekday service via the Franklin/Foxboro Line, at Foxboro station. The
Gillette_Stadium
Adjusting pitches of guitar strings
tuning and all-fourths tuning, which are regular tunings maintaining the same musical interval between consecutive open string notes. When barring each fret
Guitar_tunings
Australian tennis player
during the 1976 US Open final that she was pregnant and after one more tournament for the year, she did not play again on the regular tour until the summer
Evonne_Goolagong_Cawley
Algebraic variety defined within an affine space
algebraic sets is an affine algebraic set). The Zariski topology can also be described by way of basic open sets, where Zariski-open sets are countable
Affine_variety
British actor (born 1992)
on-screen career starring in The Cut and EastEnders: E20, later securing a regular role as Neil Cooper in the soap opera Hollyoaks and Ryan Sinclair in Doctor
Tosin_Cole
Diagram that shows all possible logical relations between a collection of sets
map) Spherical octahedron – A stereographic projection of a regular octahedron makes a three-set Venn diagram, as three orthogonal great circles, each dividing
Venn_diagram
Branch of topology
the concept of open sets. If we change the definition of 'open set', we change what continuous functions, compact sets, and connected sets are. Each choice
General_topology
Canadian chef, restaurateur, producer, vocalist and internet personality (born 1982)
a history of substance abuse. He first tried cocaine in grade 11. His regular use of the drug would lead him to a heart attack at the age of 29. Matheson
Matty_Matheson
Set whose elements all belong to another set
In mathematics, a set A is a subset of a set B if and only if all elements of A are also elements of B; B is then a superset of A. It is possible for A
Subset
Upcoming video game
Series X/S. Grand Theft Auto VI is a single-player, action-adventure game set within an open world. Its fictional US state of Leonida, based on Florida, includes
Grand_Theft_Auto_VI
Collection of open sets used to define a topology
a family B {\displaystyle {\mathcal {B}}} of open subsets of X {\displaystyle X} such that every open set of the topology is equal to the union of some
Base_(topology)
regular local ring, contains a non-empty open subset, a J-1 ring is a ring such that the set of regular points is an open subset, and a J-2 ring is a ring such
J-2_ring
Open access distributed with no fees to author and reader
Alternative labels include platinum open access, non-commercial open access, cooperative open access or, more recently, open access commons. While these terms
Diamond_open_access
Roman catholic religious order
Saint Anthony, Order of Saint Anthony or Canons Regular of Saint Anthony of Vienne (Canonici Regulares Sancti Antonii, or CRSAnt), also Antonines or Antonites
Hospital Brothers of Saint Anthony
Hospital_Brothers_of_Saint_Anthony
Italian tennis player (born 2001)
the Australian Open. He faced Carlos Alcaraz in the finals of each of the remaining majors, including a five-set loss at the French Open, and won his fourth
Jannik_Sinner
Financial services term to allow sharing of financial data
Latin American country to implement open banking legislation. On 9 March 2018, the Fintech Law of 2018 (Ley para Regular las Instituciones de Tecnología Financiera)
Open_banking
Tennis rivalry
the U.S. Open and defeated him in straight sets, on clay. Connors defeated Borg again at the U.S. Open again in 1976, this time in a four-set final, capturing
Borg–Connors_rivalry
Serbian tennis player (born 1987)
the US Open, where he had five set points in the first set and two in the second set, but lost them all before losing the match in straight sets to the
Novak_Djokovic
American tennis player (born 2002)
the US Open on August 14. He lost in the first round, in five sets, to Nuno Borges while also recording the second fastest serve of the US Open tournament
Ben_Shelton
Swedish tennis player (born 1956)
trying mid-way through the second set". At the US Open, Borg lost in the second round to Vijay Amritraj in five sets which was "one of the memorable matches
Björn_Borg
Covering by shapes without overlaps or gaps
special kinds include regular tilings with regular polygonal tiles all of the same shape, and semiregular tilings with regular tiles of more than one
Tessellation
English rock band
audience would watch as Pink tore down the wall, once again becoming a regular and caring person. During the recording of The Wall, the band became dissatisfied
Pink_Floyd
Example of topological space
completely Hausdorff. Since it has a base of regular open sets, it is an example of a semiregular space that is not regular. In terms of compactness, the space
Double_origin_topology
Narrative technique used in television and films
with regular opens in the early 2000s, all U.S. daytime dramas are currently using cold opens.[citation needed] Typically, a soap opera cold open begins
Cold_open
English tennis player (born 2003)
final at the Ilkley Open, losing to seventh seed Tristan Schoolkate in three sets. He made his ATP Tour debut at the Eastbourne Open, losing to eighth seed
Jack_Pinnington_Jones
Way to keep track of tennis matches
2001, the US Open adopted it in 2003, and the French Open adopted it in 2007, while Wimbledon continues to use a regular tie-break set -except for the
Tennis_scoring_system
Generalization of "n-th" to infinite cases
the set of singular strong limit cardinals below κ {\displaystyle \kappa } forms a closed unbounded set. Because this club set contains no regular cardinals
Ordinal_number
Four prestigious annual tournaments in professional golf
won, but it's not like there was any set number of major tournaments." In 1960, Arnold Palmer entered The Open Championship in an attempt to emulate
Men's major golf championships
Men's_major_golf_championships
Linear operator in algebra and operator theory
}} has dense range. The resolvent set of L is the set of all regular values of L: ρ ( L ) = { λ ∈ C ∣ λ is a regular value of L } . {\displaystyle \rho
Resolvent_set
American basketball coach (born 1976)
wins set by the 1976–77 and 1984–85 Wolverines. On March 8, No. 3 Michigan defeated No. 8 Michigan State for a second time, finishing the regular season
Dusty_May
Size of a set in mathematics
approached from below using basic set-theoretic operations such as unions, limits, and powersets (more formally, a regular, limit cardinal greater than
Cardinality
Operating system
macOS is based on OpenBSD's PF firewall code, Android's Bionic C standard library is based on OpenBSD code, LLVM uses OpenBSD's regular expression library
OpenBSD
Patterns used in computer programming
the expression; thus they are not considered regular expressions, which can describe the full set of regular languages over any given finite alphabet. Globs
Glob_(programming)
Topology on prime ideals and algebraic varieties
Every regular map of varieties is continuous in the Zariski topology. In fact, the Zariski topology is the weakest topology (with the fewest open sets) in
Zariski_topology
Concept in mathematics
is regular at a point x {\displaystyle x} if, in some open affine neighborhood of x {\displaystyle x} , it is a rational function that is regular at x
Morphism of algebraic varieties
Morphism_of_algebraic_varieties
Type of website edited collaboratively
other software, such as bug tracking systems. Some wiki engines are free and open-source, whereas others are proprietary. Some permit control over different
Wiki
Free and open-source virtual private network software
VPN available to consumers. OpenVPN also supports Perfect Forward Secrecy (PFS), which regenerates encryption keys at set intervals, ensuring that even
OpenVPN
Telecommunications device
converted back into sound waves at the receiver's end. Similar to early regular landline telephones, operators of sound-powered telephones generally alert
Telephone
Video game series by Nintendo
game, 8 sets of 6, including one Remix per set. The Game Boy Advance version also includes 4 Endless Games (2 of which were adapted from regular Rhythm
Rhythm_Heaven
Golf tournament
The UNC Health Championship (formerly Rex Hospital Open) is a regular golf tournament on the Korn Ferry Tour. It is played annually at the Raleigh Country
UNC_Health_Championship
storylines contained within. There were three pilot movies, followed by 245 regular episodes over nine seasons, followed by five specials. There were typically
List of The Love Boat episodes
List_of_The_Love_Boat_episodes
Finite-state machine in automata theory
p-regular (also: a pure-group language) if it is accepted by a permutation automaton. For example, the set of strings of even length forms a p-regular language:
Permutation_automaton
Type of topology
mathematics, the compact-open topology is a topology defined on the set of continuous maps between two topological spaces. The compact-open topology is one of
Compact-open_topology
Complement of an open subset
terms of its open sets, which determine what counts as a "neighborhood" of its points. A set is closed if it is the complement of an open set. In metric
Closed_set
American soccer team
went on to dominate the regular season in the NPSL's Sunshine Conference. Only one loss to Jacksonville Armada FC in the regular season led the team to
Miami_FC
Concept in probability theory
In probability theory, regular conditional probability is a concept that formalizes the notion of conditioning on the outcome of a random variable. The
Regular conditional probability
Regular_conditional_probability
Set of a ring's prime ideals
space; that is, commutative rings are associated to every point and every open set, which satisfy some compatibility conditions. The structure formed by the
Spectrum_of_a_ring
American actor (born 1975)
in Philadelphia, for which he also writes and produces. Hornsby had a regular role on the NBC comedy-crime series Good Girls (2018–2020). He was also
David_Hornsby
Footballer (born 2005)
MLS debut that same year at the age of 15 years old and later became a regular starter for the Sounders, where he played for five seasons. In 2026, he
Obed_Vargas
Stadium in Arlington, Texas
platforms connected by stairways. The record attendance for an NFL regular season game was set in 2009 with a crowd of 105,121. It also has twin video boards
AT&T_Stadium
Sports division of the USA TV channel in the U.S.
coverage from the U.S. Open and U.S. Women's Open. In September 2025, Versant announced a new agreement with the WNBA for 50 regular season games, along
USA_Sports_(2025–present)
Linux distribution for wireless routers and embedded systems
available. OpenWrt provides regular bug fixes and security updates even for devices that are no longer supported by their manufacturers. OpenWrt provides
OpenWrt
American actress (born 1996)
animated series Tarantula. In March 2018, Gabrielle was cast as a series regular in the role of Prudence in the Netflix original series, Chilling Adventures
Tati_Gabrielle
Public research university in the UK
The Open University (OU) is a public research university and the largest university in the United Kingdom by number of students. The majority of the OU's
Open_University
American professional golfer (born 1996)
his third major at the 2025 PGA Championship and his fourth at the 2025 Open Championship. Scheffler has been named PGA Tour Player of the Year for four
Scottie_Scheffler
Type of singularity analysis
the Fourier transform of f, localized at x, is sufficiently regular when restricted to an open cone containing ξ {\displaystyle \xi } . More precisely, a
Wave_front_set
REGULAR OPEN-SET
REGULAR OPEN-SET
Boy/Male
English French
Open.
Boy/Male
English
Open.
Boy/Male
English French
Open.
Boy/Male
Welsh
Son of Owen.
Female
English
English short form of Latin Penelope, PEN means "weaver of cunning."
Surname or Lastname
English
English : variant of Penn.Dutch : metonymic occupational name for a clerk or penman, from Dutch pen ‘pen’.Cambodian : unexplained.
Boy/Male
English French
Open.
Boy/Male
English French
Open.
Boy/Male
English French
Open.
Male
Swedish
Norwegian and Swedish form of Old Norse Óðinn, ODEN means "poetry, song" and "eager, frenzied, raging."
Boy/Male
English French American
Open.
Male
English
 Anglicized form of Irish Gaelic Eóghan, OWEN means "born of yew." Compare with another form of Owen.
Boy/Male
Hindu, Indian, Tamil
Regular Winner
Male
Welsh
 Modern Welsh form of Old Welsh Owain, OWEN means "born of yew." Compare with another form of Owen.
Boy/Male
Celtic Welsh
Son of Owen.
Male
Welsh
Variant form of Welsh Owen, possibly OUEN means "born of yew."
Boy/Male
English French
Open.
Girl/Female
Hebrew
Precious.
Female
Thai/Siamese
Thai name PEN-CHAN means "full moon."
Boy/Male
French
Open.
REGULAR OPEN-SET
REGULAR OPEN-SET
Surname or Lastname
English (of Welsh origin)
English (of Welsh origin) : variant of Powell, with redundant English patronymic -s.English : patronymic from Poul, a variant of the personal name Paul.
Boy/Male
Australian, British, English
Reality
Male
Egyptian
, Horus the Executer of Justice.
Girl/Female
Hindu, Indian, Tamil
One with Beautiful Eyes
Girl/Female
French Latin Italian
Jewel.
Boy/Male
Arabic
King; Leader; Fire
Girl/Female
Tamil
Dayashree | தயாஷà¯à®°à¯€Â
Masterful teacher
Girl/Female
Tamil
Trivani | தà¯à®°à¯€à®µà®¾à®¨à¯€Â
Goddess Durga
Boy/Male
Tamil
No obstacles, Calm, Happy, Goddess of wealth
Male
Hebrew
(×¢Ö²×“Ö´×™× ï‹) Hebrew name ADIYNOW means "soft, delicate" or "his ornament." In the bible, this is the name of one of King David's warriors.
REGULAR OPEN-SET
REGULAR OPEN-SET
REGULAR OPEN-SET
REGULAR OPEN-SET
REGULAR OPEN-SET
a.
Conformed to a rule; agreeable to an established rule, law, principle, or type, or to established customary forms; normal; symmetrical; as, a regular verse in poetry; a regular piece of music; a regular verb; regular practice of law or medicine; a regular building.
a.
Produced by an open string; as, an open tone.
a.
Open.
a.
Not drawn together, closed, or contracted; extended; expanded; as, an open hand; open arms; an open flower; an open prospect.
a.
Constituted, selected, or conducted in conformity with established usages, rules, or discipline; duly authorized; permanently organized; as, a regular meeting; a regular physican; a regular nomination; regular troops.
a.
Thorough; complete; unmitigated; as, a regular humbug.
n.
One who is not regular; especially, a soldier not in regular service.
a.
Not concealed or secret; not hidden or disguised; exposed to view or to knowledge; revealed; apparent; as, open schemes or plans; open shame or guilt.
a.
Not settled or adjusted; not decided or determined; not closed or withdrawn from consideration; as, an open account; an open question; to keep an offer or opportunity open.
a.
Belonging to a monastic order or community; as, regular clergy, in distinction dfrom the secular clergy.
a.
Having all the parts of the same kind alike in size and shape; as, a regular flower; a regular sea urchin.
v. t.
To make or set open; to render free of access; to unclose; to unbar; to unlock; to remove any fastening or covering from; as, to open a door; to open a box; to open a room; to open a letter.
a.
Not regular; not conforming to a law, method, or usage recognized as the general rule; not according to common form; not conformable to nature, to the rules of moral rectitude, or to established principles; not normal; unnatural; immethodical; unsymmetrical; erratic; no straight; not uniform; as, an irregular line; an irregular figure; an irregular verse; an irregular physician; an irregular proceeding; irregular motion; irregular conduct, etc. Cf. Regular.
v. t.
To enter upon; to begin; as, to open a discussion; to open fire upon an enemy; to open trade, or correspondence; to open a case in court, or a meeting.
a.
Governed by rule or rules; steady or uniform in course, practice, or occurence; not subject to unexplained or irrational variation; returning at stated intervals; steadily pursued; orderlly; methodical; as, the regular succession of day and night; regular habits.
v. t. & i.
To open.
n.
Open or unobstructed space; clear land, without trees or obstructions; open ocean; open water.
v. t.
To spread; to expand; as, to open the hand.
a.
Free or cleared of obstruction to progress or to view; accessible; as, an open tract; the open sea.
a.
Free; disengaged; unappropriated; as, to keep a day open for any purpose; to be open for an engagement.