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mathematics, the term essentially unique is used to describe a weaker form of uniqueness, where an object satisfying a property is "unique" only in the sense
Essentially_unique
Topics referred to by the same term
Look up unique or uniqueness in Wiktionary, the free dictionary. Unique primarily refers to: Uniqueness, a state or condition wherein something is unlike
Unique
Logical quantifier
uniqueness is "uniqueness up to equality"). This is called essentially unique. For example, many concepts in category theory are defined to be unique
Uniqueness_quantification
Index of articles associated with the same name
finite group theory. The word unique is sometimes replaced by essentially unique, whenever one wants to stress that the uniqueness is only referred to the underlying
Uniqueness_theorem
Polynomial without nontrivial factorization
polynomials, such as the essentially unique factorization into prime or irreducible factors. When the coefficient ring is a field or other unique factorization domain
Irreducible_polynomial
Integers have unique prime factorizations
unique factorization theorem and prime factorization theorem, states that every integer greater than 1 is either prime or can be represented uniquely
Fundamental theorem of arithmetic
Fundamental_theorem_of_arithmetic
Concept in topology
subgroups of Lie groups are not in general unique, but are unique up to conjugation – they are essentially unique. An example would be the subgroup O(2),
Maximal_compact_subgroup
Subclass of manifold
group. These manifolds are uniquely determined by their fundamental groups. They can all be represented in an essentially unique way as Seifert fiber spaces:
Spherical_3-manifold
Algebraic curve in projective 3-space
projective 3-space P3. It is a fundamental example of a skew curve. It is essentially unique, up to projective transformation (the twisted cubic, therefore). In
Twisted_cubic
Indian national identification number
Aadhaar is a twelve-digit unique identity number that can be obtained voluntarily by all residents of India based on their place of residence, biometrics
Aadhaar
Philosophical concept
isolation is the subjective feeling that every human life experience is essentially unique and can be understood only by themselves, creating a gap between a
Existential_isolation
Any topological 3-manifold has unique PL and smooth structures
Moise in Moise (1952), states that any topological 3-manifold has an essentially unique piecewise-linear structure and smooth structure. The analogue of Moise's
Moise's_theorem
Mathematic theorem about Riemann surfaces
differential geometry, and showed that the stable vector bundles have an essentially unique unitary connection of constant (scalar) curvature. In the degree zero
Narasimhan–Seshadri_theorem
Number in {..., –2, –1, 0, 1, 2, ...}
any positive integer can be written as the products of primes in an essentially unique way. This is the fundamental theorem of arithmetic. Z {\displaystyle
Integer
Mathematical structure
one might express this by saying that the smooth structure is (essentially) unique. The case for k = 0 is different. Namely, there exist topological
Differential_structure
Measurability theorem
set for μ {\displaystyle \mu } . Moreover, this decomposition is essentially unique, meaning that for any other pair ( P ′ , N ′ ) {\displaystyle (P'
Hahn_decomposition_theorem
Linear operator equal to its own adjoint
is essentially self-adjoint if it has a unique self-adjoint extension. In practical terms, having an essentially self-adjoint operator is almost as good
Self-adjoint_operator
Most general completion of a commutative square given two morphisms with same codomain
pullback of two morphisms f and g need not exist, but if it does, it is essentially uniquely defined by the two morphisms. In many situations, X ×Z Y may intuitively
Pullback_(category_theory)
Problem that is difficult or impossible to solve
operations that may be incorporated into the plan. Every wicked problem is essentially unique. Every wicked problem can be considered to be a symptom of another
Wicked_problem
Boolean algebra with all operators and laws forming a complete logical system
set theory in the theory of forcing. Every Boolean algebra A has an essentially unique completion, which is a complete Boolean algebra containing A such
Complete_Boolean_algebra
Country in East Asia
Chuan (Sichuan), and Yue (Guangdong). Chinese Buddhists have developed a unique cuisine that avoids meat, while Chinese Islamic cuisine excludes pork and
China
Sculpture in Singapore
2022. "All the Essentially Essential". Roots. National Heritage Board. Retrieved 30 April 2022. Khoe, Megan (7 July 2021). "16 Unique Sculptures In Singapore
All_the_Essentially_Essential
Unsolved problem in computational complexity theory
science Is the Unique Games Conjecture true? More unsolved problems in computer science In computational complexity theory, the unique games conjecture
Unique_games_conjecture
Ability of a computing system to simulate Turing machines
computation. The work of Gödel showed that the notion of computation is essentially unique. In 1941 Konrad Zuse completed the Z3 computer. Zuse was not familiar
Turing_completeness
Country in South Asia
societies, the "caste system" is uniquely developed in Hindu societies." Gupta 2008 "Caste: What makes Indian society unique is the phenomenon of caste. Economic
India
Composed chess endgame position
rather than played in an actual game—where the goal is to find the essentially unique way for one side (usually White) to win or draw, as stipulated, against
Endgame_study
Special objects used in (mathematical) category theory
they do exist, they are essentially unique. Specifically, if I1 and I2 are two different initial objects, then there is a unique isomorphism between them
Initial_and_terminal_objects
Smooth manifold that is homeomorphic but not diffeomorphic to a sphere
dimension 3, Edwin E. Moise proved that every topological manifold has an essentially unique smooth structure (see Moise's theorem), so the monoid of smooth structures
Exotic_sphere
Proposition in mathematics that is unproven
has coefficients derived from the numbers Nk of points over the (essentially unique) field with qk elements. Weil conjectured that such zeta-functions
Conjecture
Characterizing property of mathematical constructions
{\displaystyle (A,u)} does exist, then it is essentially unique. Specifically, it is unique up to a unique isomorphism: if ( A ′ , u ′ ) {\displaystyle
Universal_property
Equation for function that computes iterated values
{\displaystyle h(y)<y} for all y {\displaystyle y} . The solution is essentially unique in the sense that there exists a canonical solution α 0 {\displaystyle
Abel_equation
Country in Eurasia from 1922 to 1991
bureaucratic collectivism, state capitalism, state socialism, or a totally unique mode of production. The USSR implemented a broad range of policies over
Soviet_Union
Mathematical space
Edwin E. Moise in, states that any topological 3-manifold has an essentially unique piecewise-linear structure and smooth structure. As corollary, every
3-manifold
Mathematical space
most 6, any piecewise linear (PL) structure can be smoothed in an essentially unique way, so in particular the theory of 4 dimensional PL manifolds is
4-manifold
Word with multiple distinct meanings
cyclic shifts". Look up modulo in Wiktionary, the free dictionary. Essentially unique List of mathematical jargon Up to "Modular arithmetic". Encyclopedia
Modulo_(mathematics)
Medical condition caused by receiving too little or too many nutrients
largely determines energy requirements, is difficult to estimate. Women have unique nutritional requirements, and in some cases need more nutrients than men;
Malnutrition
Mathematical concept
if a diagram does have a limit then this limit is essentially unique: it is unique up to a unique isomorphism. For this reason one often speaks of the
Limit_(category_theory)
complete. If it is not, then it can be completed: one can find an essentially unique complete topological ring S {\displaystyle S} that contains R {\displaystyle
Topological_ring
Mathematical statement of uniqueness, except for an equivalent structure
in Wiktionary, the free dictionary. Abuse of notation Adequality Essentially unique List of mathematical jargon Quotient group Quotient set Nekovář, Jan
Up_to
Excess of a non-negative real number beyond its integer part
{\displaystyle \{x\}:=x-\lfloor x\rfloor .} Every real number can be essentially uniquely represented as a simple continued fraction, namely as the sum of
Fractional_part
Type of group in mathematics
_{1\leq i\leq n}\mathrm {C} _{{p_{i}}^{m_{i}}}.} This expression is essentially unique: there is a bijection between the sets of groups in two such expressions
Primary_cyclic_group
American mathematician (1918–1998)
proved Moise's theorem that every 3-manifold can be triangulated in an essentially unique way. Moïse joined the School Mathematics Study Group when it started
Edwin_E._Moise
American multinational technology company
Google Sheets and Google Slides, with additional administrative tools, unique domain names, and 24/7 support. On September 24, 2012, Google launched Google
Hungarian mathematician (1895–1965)
University in 1948. In the 1920s, he proved that surfaces have an essentially unique triangulation. In 1933, Radó published "On the Problem of Plateau"
Tibor_Radó
American singer and songwriter (born 1979)
Queen". Rolling Stone. Retrieved September 1, 2023. "PSP GOES P!NK – In a Unique Collaboration with the Artist P!nk". GamesIndustry.biz. August 23, 2006
Pink_(singer)
Category in mathematics
∞-category is canonically triangulated, and moreover mapping cones become essentially unique (in a precise homotopical sense). Moreover, a stable ∞-category naturally
Triangulated_category
Island country in Southeast Asia
corrupt countries in the world, in spite of being illiberal. Singapore's unique combination of a strong, soft-authoritarian government with an emphasis
Singapore
Country in Southern and Western Europe
roots. Spain's extensive history with many cultural influences has led to a unique cuisine. In particular, three main divisions are easily identified: Mediterranean
Spain
an irreducible representation of dimension greater than 1 has an essentially unique Kirillov model. Over a local field, the space of functions with compact
Kirillov_model
Web browser developed by Google
demonstration of Chrome. Afterward, Schmidt said, "It was so good that it essentially forced me to change my mind." In September 2004, rumors of Google building
Google_Chrome
Topological manifold whose homology coincides with that of a sphere
can be written as a connected sum of prime homology 3-spheres in an essentially unique way. (See Prime decomposition (3-manifold).) Suppose that a 1 , …
Homology_sphere
American businessman and investor (1955–2011)
oversaw the development of its unusual case and Rod Holt developed the unique power supply. During the design stage, Jobs argued that the Apple II should
Steve_Jobs
Sequence of spaces in linear algebra
is almost never unique (the counterexamples are trivial); see below. A complete flag on an inner product space has an essentially unique orthonormal basis:
Flag_(linear_algebra)
Portuguese footballer (born 1985)
which involves him standing with his legs far apart. Regarding Ronaldo's unique style of taking free kicks, former United assistant manager Mike Phelan
Cristiano_Ronaldo
Branch of topology
vanishes. In dimension 3 and lower, every topological manifold admits an essentially unique PL structure. In dimension 4 there are many examples with vanishing
Low-dimensional_topology
Matrix in math with special properties
matrix of that order exists. Order 66 seems to be an open problem. The essentially unique conference matrix of order 6 is given by ( 0 + 1 + 1 + 1 + 1 + 1 +
Conference_matrix
Concept in homological algebra
truncation functors, such functors can always be constructed and are essentially unique. Suppose that D {\displaystyle {\mathcal {D}}} is a triangulated category
T-structure
Decomposition in multilinear algebra
tensor A {\displaystyle {\mathcal {A}}} are called identifiable or essentially unique. A rank- r {\displaystyle r} tensor A ∈ F I 1 ⊗ F I 2 ⊗ ⋯ ⊗ F I M
Tensor_rank_decomposition
quasi-Fuchsian group of the first kind. The quasi-Fuchsian group is essentially uniquely determined by the two Riemann surfaces, so the space of marked quasi-Fuchsian
Simultaneous uniformization theorem
Simultaneous_uniformization_theorem
Two-dimensional manifold
metric on an oriented, closed surface is conformally equivalent to an essentially unique metric of constant curvature. This provides a starting point for one
Surface_(topology)
Country within the United Kingdom
Courts from 2008 to 2010. For three centuries the Scots legal system was unique for being the only national legal system without a parliament. This ended
Scotland
Group in mathematical representation theory
The Stone–von Neumann theorem states that this representation is essentially unique: if ρ ′ {\displaystyle \rho '} is another such representation, there
Metaplectic_group
American theoretical physicist (1904–1967)
produced a sense of direct participation in all of us; it created that unique atmosphere of enthusiasm and challenge that pervaded the place throughout
J._Robert_Oppenheimer
First-century Jewish preacher and religious leader
miracles. Scholar Paul J. Achtemeier argues that such miracles were not unique to Jesus in the ancient world and were perceived as ambiguous even by eyewitnesses
Jesus
Online biomedical database
formatting formal queries. A PMID (PubMed identifier or PubMed unique identifier) is a unique integer value, starting at 1, assigned to each PubMed record
PubMed
Chinese harvest festival
toad until water was sprinkled on his head, in which he would then stop. A unique tradition is celebrated quite exclusively in the island city of Xiamen.
Mid-Autumn_Festival
Model of a class of bargaining games
while player 2 gets d/(1+d). This subgame perfect equilibrium is essentially unique. When the discount factor is different for the two players, d 1 {\displaystyle
Rubinstein_bargaining_model
Political party
change denial in opposition to the general scientific consensus, making them unique even among other worldwide conservative parties. In 2006, then-California
Republican Party (United States)
Republican_Party_(United_States)
Subfamily of wasps
exodont, opening outwards and not overlapping. This characteristic is essentially unique among braconids, with only a few rare exceptions (e.g., the genus
Alysiinae
Country in South Asia
activities. The first two decades in the 20th century are noted by the unique harmony among Sinhalese and Tamil political leadership, which has since
Sri_Lanka
1983 video game
many aspects which, at that early period in gaming history, were essentially unique to itself, such as an encounter with a tribe of cannibalistic headhunters
Valley_of_the_Minotaur
Ancient Indo-Aryan language of South Asia
traditions and an admixture of various regional dialects. Each language has some unique and regionally creative aspects, with unclear origins. Prakrit languages
Sanskrit
Section of the field on an escutcheon
Cheesman: per pale and per pall. This is to be distinguished from the essentially unique partition in the arms of the 2nd Weather Group of the United States
Division_of_the_field
NFL team in Green Bay, Wisconsin
into the Pro Football Hall of Fame. *Interim head coaches The Packers are unique in having their market area cover two media markets, both Green Bay and
Green_Bay_Packers
American civil rights activist (1925–1965)
teachings varied from those of other Muslims because they were adapted to the "uniquely pitiful" condition of black people in the United States. He taught that
Malcolm_X
Jewish nationalist movement
nationhood the Judaic sense of being a nation was rooted in religious beliefs of unique chosenness and divine providence, rather than in ethnicity. Specifically
Zionism
Star in the constellation Eridanus
remnant doesn't fit into any commonly used category, and is as such essentially unique. It is hypothesized that 500 million years ago, the white dwarf started
EF_Eridani
Data item stored in a browser by a website
Microsoft websites in August 2011: cookie syncing that respawned MUID (machine unique identifier) cookies, and ETag cookies. Due to media attention, Microsoft
HTTP_cookie
Duality for locally compact abelian groups
a locally compact group G {\displaystyle G} is that it carries an essentially unique natural measure, the Haar measure, which allows one to consistently
Pontryagin_duality
American mathematician
theorem, which states that every 3-manifold can be triangulated in an essentially unique way. In 1959, Bing published an independent proof of the triangulation
R._H._Bing
Mesoamerican civilization (c. 2000 BC – 1697 AD)
art tradition in the Americas. Maya art has many regional styles, and is unique in the ancient Americas in bearing narrative text. The finest surviving
Maya_civilization
Structure group sub-bundle on a tangent frame bundle
structure group do not always exist. If they exist, they are usually not essentially unique, since the isomorphism ϕ {\displaystyle \phi } is an important part
G-structure_on_a_manifold
Unrecognised state in Southern Africa (1965–1979)
Rhodesia was not developed as an indigenous African territory, but rather as a unique state that reflected its multiracial character. This situation made it different
Rhodesia
2017 Marvel Studios film
for the next movie? I don't know, but it will force us to do something unique." Goldstein added that it "diminishes what is often the most trivial part
Spider-Man:_Homecoming
Generalization of the concept of vector bundle
This neighborhood is unique up to isotopy. Thus every microbundle can be refined to an actual fiber bundle in an essentially unique way. Taking the fiber
Microbundle
Ailment in horses
1.0, leading to the numerous EFL and LFL events and the rare but essentially unique single-eye events of MRLS. A poor immune response in affected tissues
Mare reproductive loss syndrome
Mare_reproductive_loss_syndrome
Topological algebra associated to continuous groups
discrete group. If G is a locally compact Hausdorff group, G carries an essentially unique left-invariant countably additive Borel measure μ called a Haar measure
Group algebra of a locally compact group
Group_algebra_of_a_locally_compact_group
Global system of connected computer networks
years, especially in Asia and the Pacific and in Africa. The number of unique mobile cellular subscriptions increased from 3.9 billion in 2012 to 4.8 billion
Internet
2009 film by Gavin Hood
ever played. As a child, he loved the Wolverine comics because of their unique "urban sensibility". Schreiber had studied to be a fight choreographer and
X-Men_Origins:_Wolverine
Tribe of bees
relationship between male euglossine bees and volatile chemicals is essentially unique in the animal kingdom. Scientists use single synthetic compounds as
Euglossini
English rock band
clear that I'm not here." Author Patrick Croskery described Animals as a unique blend of the "powerful sounds and suggestive themes" of Dark Side with The
Pink_Floyd
Correspondence in functional analysis
-algebra A {\displaystyle A} , the corresponding GNS representation is essentially uniquely determined by the condition, ρ ( a ) = ⟨ π ( a ) ξ , ξ ⟩ {\displaystyle
Gelfand–Naimark–Segal construction
Gelfand–Naimark–Segal_construction
Bat-and-ball game
hitter's park, if one or the other discipline notably benefits from its unique mix of elements. The most exceptional park in this regard is Coors Field
Baseball
Wavelet constructed using a spline function
interval [ 0 , 2 m − 1 ] {\displaystyle [0,2m-1]} . These wavelets are essentially unique in a certain sense explained below. The compactly supported B-spline
Spline_wavelet
Disputed territory in north-western Africa
indigenous Berber tribes mixed with the Maqil Arab tribes and formed a culture unique to Morocco and Mauritania.[citation needed] The Spanish presence in the
Western_Sahara
Lower house of the U.S. Congress
(Hawaii and New Mexico) used multi-member districts in 1967. Louisiana is unique in that it holds a jungle primary election on the general Election Day with
United States House of Representatives
United_States_House_of_Representatives
Spiritual practices from ancient India
defined as "seeing things as they truly are" (yathābhūtaṃ darśanam). A unique feature of classical Buddhism is its understanding of all phenomena (dhammas)
Yoga
Philosophical study of morality
moral properties are unique because they express what should be the case. Proponents of this position often emphasize this uniqueness by claiming that it
Ethics
American singer-songwriter (born 1941)
in the history of American music." Obama praised Dylan's voice for its "unique gravelly power that redefined not just what music sounded like but the message
Bob_Dylan
1932–1945 Japanese puppet state in northern China
after the French legal system, but there were a number of particularities unique to Manchukuo. Law students were trained to write essays on such topics as
Manchukuo
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