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Class equipped with a preorder
In mathematics, a preordered class is a class equipped with a preorder. When dealing with a class C, it is possible to define a class relation on C as
Preordered_class
Reflexive and transitive binary relation
a,b\in X.} A preordered class is a class equipped with a preorder. Every set is a class and so every preordered set is a preordered class. Preorders play
Preorder
Category where each homset contains at most one morphism
most one morphism. As such, a thin category amounts to a preordered class (or a preordered set, if its objects form a set). A thin category that is skeletal
Thin_category
Algebraic object with an ordered structure
{\displaystyle -1} is not in P . {\displaystyle P.} A preordered field is a field equipped with a preordering P . {\displaystyle P.} Its non-zero elements P
Ordered_field
a closed preordered set is one whose anti-well-ordered subsets have lower bounds. Let κ {\displaystyle \kappa } be a cardinal. A preordered set ( P ,
Closed_preordered_set
Category admitting tensor products
very similar to representation categories of linear algebraic groups. A preordered monoid is a monoidal category in which for every two objects c , c ′ ∈
Monoidal_category
Type of topology in mathematics
is canonically associated to a preordered set by taking the open sets to be the upper sets. Conversely, the preordered set can be recovered from the Alexandrov
Alexandrov_topology
Vector space with a partial order
{\displaystyle X,} the pair ( X , ≤ ) {\displaystyle (X,\leq )} is called a preordered vector space and we say that the preorder ≤ {\displaystyle \,\leq \,}
Ordered_vector_space
Topics referred to by the same term
"KORD"), an airport in Chicago, US Ord, the category of preordered sets Ord, the proper class of all ordinal numbers ord(V), the order type of a well-ordered
Ord
Algorithm to search the nodes of a graph
reverse preordering is the reverse of a preordering, i.e. a list of the vertices in the opposite order of their first visit. Reverse preordering is not
Depth-first_search
Concept in functional analysis
a positive linear operator from an preordered vector space ( X , ≤ ) {\displaystyle (X,\leq )} into a preordered vector space ( Y , ≤ ) {\displaystyle
Positive_linear_operator
2011 video game
Players who preordered before November 2, 2014, received an experience boost that granted twelve times multiplicative experience for class-related missions
Star_Wars:_The_Old_Republic
Collection of objects and morphisms
category is called the free category generated by the graph. The class of all preordered sets with order-preserving functions (i.e., monotone-increasing
Category_(mathematics)
American singer-songwriter (born 1942)
than a hastily assembled collection of songs.[citation needed] Capitol preordered 500,000 copies—the largest pressing of a debut album in the label's prior
Bobbie_Gentry
Particular correspondence between two partially ordered sets
mathematician Évariste Galois. A Galois connection can also be defined on preordered sets or classes; this article presents the common case of posets. The literature
Galois_connection
Extreme element of a preorder
order theory, a maximal element of a subset S {\displaystyle S} of some preordered set is an element of S {\displaystyle S} that is not smaller than any
Maximal_and_minimal_elements
Algebraic structure
frames corresponding to interior algebras are precisely the preordered sets. Preordered sets (also called S4-frames) provide the Kripke semantics of
Interior_algebra
Hong Kong scale model manufacturer
figurines of licensed properties, like Marvel and Star Wars, which must be preordered. Hot Toys collectibles are primarily available to purchase from secondary
Hot_Toys
2008 video game
Ricardo Sanchez, with art by Neil Googe for those who preordered. Also for those who preordered gained a 3 day head start before launch. Aion was in available
Aion_(video_game)
Formal semantics for non-classical logic systems
\rangle } , where ⟨ W , ≤ ⟩ {\displaystyle \langle W,\leq \rangle } is a preordered Kripke frame, and ⊩ {\displaystyle \Vdash } satisfies the following conditions:
Kripke_semantics
1985 Japanese manga series and its franchise
were released in the 1980s, but as so-called "Coterie" games, which are preordered editions and only go on limited sale at Japan's Game Market trade show
Area_88
Seventh generation of BMW 5 Series
offered in both rear-wheel drive and all-wheel drive (xDrive) variants. Preordered 530e LCI models come without the hybrid blue inserts for the BMW logos
BMW_5_Series_(G30)
2023 studio album by Dropkick Murphys
Patrick's Day shows in the US, which begin in March 2023. For people who preordered the vinyl version of Okemah Rising through the band's website, received
Okemah_Rising
Mathematical set with an ordering
acyclic graphs) are called topological sorting. Every poset (and every preordered set) may be considered as a category where, for objects x {\displaystyle
Partially_ordered_set
Chinese automobile manufacturing company
on 5 August 2025. Retrieved 25 June 2026. "Chery New Energy launches preordering for its Tiggo e". MarkLines Automotive Industry Portal. 31 July 2019
Chery
2005 novel by Robert Jordan
available online. Additionally, a promotion at Amazon.com allowed those who preordered Knife of Dreams from August 10 to October 10, 2005 to immediately download
Knife_of_Dreams
Disturbed Pack 01) were offered at no cost in June 2008 to customers who preordered the band's album Indestructible through Best Buy's online store. Crüe
List of downloadable songs for the Rock Band series
List_of_downloadable_songs_for_the_Rock_Band_series
2021 French/Belgian film
and cook for the finest of French palates. Among a multitude of classic preordered dishes served, he serves one small creation of his own (the small pastry
Delicious_(2021_film)
Extension of rough set theory
the domain of a criterion q ∈ Q {\displaystyle q\in Q} is completely preordered by an outranking relation ⪰ q {\displaystyle \succeq _{q}} ; x ⪰ q y {\displaystyle
Dominance-based rough set approach
Dominance-based_rough_set_approach
2011 video game
released, along with content that was originally reserved for those who preordered the game. A new wave-based game mode called "Exterminatus" was also made
Warhammer 40,000: Space Marine
Warhammer_40,000:_Space_Marine
Topics referred to by the same term
(geometry), the set of all planes through a given line Fan (order), a class of preorderings on a field FAN algorithm, an algorithm for automatic test pattern
Fan
Motor vehicle
Edition 1.9 JTDm was produced for the British market, where it had to be preordered by the customer. Its unofficial name was "quadrifoglio verde" (cloverleaf)
Alfa_Romeo_GT
2007 real-time strategy video game
Conflict exclusive Creative HS-390 headset (Europe Only). Those who had preordered the game were given access to the Beta, the ability to preserve their
World_in_Conflict
2007 video game
2—which earned $125 million within 24 hours of its launch. The game was preordered by more than one million people in North America. Worldwide more than
Halo_3
2013 video game
served as a prequel, and players who preordered the game gained access to "Codebreakers". Those who preordered the game using GAME unlocked the Light
The_Bureau:_XCOM_Declassified
Mathematical proposition equivalent to the axiom of choice
choice in the preceding section. There is a version of Zorn's lemma for a preordered set. In that case, we need to be a bit careful about the definition of
Zorn's_lemma
Japanese subcompact hatchback
of each RS model), these limited edition vehicles quickly sell out. Preordering is available at each dealership on a first-come, first-served basis.
Scion_xA
Vaccine against SARS-CoV-2
workers. By December 2020, more than 10 billion vaccine doses had been preordered, with about half of the doses purchased by high-income countries comprising
COVID-19_vaccine
2009 video game
between standard and guitar controllers, so he abandoned it. Players who preordered the game through GameStop were able to unlock a special promotional in-game
Brütal_Legend
Mobile operating system
The first 450 telephones were sold at this event, while the rest of the preordered devices were shipped shortly after. In August 2015, version 1.1.9 "Eineheminlampi"
Sailfish_OS
2012 video game
and Ignition in the Deep and a flare gun for multiplayer. Players who preordered the game at GameStop gained access to the "Monkey Business Pack", which
Far_Cry_3
2019 video game
January 2026, it has not been released. Katana Zero was Devolver's most-preordered Switch game, sold over 100,000 copies within a week of release, and became
Katana_Zero
2007 fantasy novel by J. K. Rowling
Collector's Edition".[citation needed] According to CNN, this was the most preordered book of 2016. Attributed to multiple references: Attributed to multiple
Harry Potter and the Deathly Hallows
Harry_Potter_and_the_Deathly_Hallows
2011 video game
but was sold out before March 2011. After the game's launch, those who preordered the Nano Edition had their shipment delayed. EA gave the affected customers
Crysis_2
2000 video game
art book, and a clock shaped like the character Quickie. Players who preordered the game in participating Sofmap electronics stores also received an alarm
Tales_of_Eternia
American hip-hop duo
Link: Lost was made available for digital download preorder. Those who preordered on that day received the first single off the album, titled "Vomit". The
Insane_Clown_Posse
2010 action role-playing game
2010; in Europe on May 28; and in North America on June 1. Players who preordered the game via GameStop and Best Buy received the "Exclusive Assault Pack"
Alpha_Protocol
2016 video game
limited edition Early Adopters Box version was available to those that preordered the game, including the Space Marine faction from the start. The first
Battlefleet_Gothic:_Armada
Algebraic structure with an associative operation and an identity element
written additively. Any commutative monoid is endowed with its algebraic preordering ≤, defined by x ≤ y if there exists z such that x + z = y. An order-unit
Monoid
Algebraic concept in measure theory, also referred to as an algebra of sets
\leq ,{\mathcal {F}})} where ( X , ≤ ) {\displaystyle (X,\leq )} is a preordered set and ( X , F ) {\displaystyle (X,{\mathcal {F}})} is a field of sets
Field_of_sets
Transformation of one computational problem to another
squaring. This corresponds to many-one reduction. Reducibility is a preordering, that is, a reflexive and transitive relation, on P(N)×P(N), where P(N)
Reduction_(complexity)
2012 video game
option to customize the aesthetic design of soldiers' armor. Players who preordered on Steam also received bonus items for Valve Corporation's video game
XCOM:_Enemy_Unknown
Analysis of datasets using techniques from topology
made in Bubenik et al., the indexing category P {\textstyle P} is any preordered set (not necessarily N {\displaystyle \mathbb {N} } or R {\displaystyle
Topological_data_analysis
Type of mathematical function
y'(x)=\left(x\mapsto -{\sqrt {2}}\right)'=0} . For functions between preordered sets, constant functions are both order-preserving and order-reversing;
Constant_function
Generalization of category
(2, 1)-category. The category Ord of preordered sets is a 2-category since each hom-set has a natural preordered structure; thus a category structure
2-category
October 2015: Makuch, Eddie (20 August 2015). "Get $20 Virtual Cash for Preordering Guitar Hero Live". GameSpot. Retrieved 25 November 2015. 4 November 2015:
List of songs in Guitar Hero Live
List_of_songs_in_Guitar_Hero_Live
Mathematical concept
uniquely determined by ≤. Going in the other direction, suppose (X, ≤) is a preordered set. Define a topology τ on X by taking the open sets to be the upper
Finite_topological_space
Special subset of a partially ordered set
Thus passage from prefilter to filter is an instance of passing from a preordering to associated partial ordering. Historically, filters generalized to
Filter_(mathematics)
Japanese musician (1966–2011)
on September 26, 2012. Taiji plays on four of its songs, and those who preordered the album received a bonus CD that features two demo tracks he also plays
Taiji_(musician)
Social psychology concept
differently as distance increases or decreases. When pre-purchasing or preordering an item far in the future the consumer may regret or change their decision
Construal_level_theory
Canadian animated sitcom (2005–2011)
and tells him if he goes out on a date with her, she would give him a preordered copy of Carl's favorite game, which he dearly wants. As a back-up solution
Carl2
Branch of mathematics
does not have to be a lower set. Furthermore, it is often generalized to preordered sets. A subset which is – as a sub-poset – linearly ordered, is called
Order_theory
Distribution and administration of COVID-19 vaccinations
some 16 countries representing only 14% of the world's population had preordered more than 10 billion vaccine doses or about 51% of the available world
Deployment of COVID-19 vaccines
Deployment_of_COVID-19_vaccines
Theorem in economics
MUR if-and-only-if (X, ⪰ {\displaystyle \succeq } ) is a semi-normally-preordered topological space. If X is a locally compact and sigma-compact Hausdorff
Utility representation theorem
Utility_representation_theorem
Glossary of terms used in branch of mathematics
an acyclic binary relation (also called an acyclic digraph). Preordered set. A preordered set ( P , ≤ ) {\displaystyle (P,\leq )} is a set P {\displaystyle
Glossary_of_order_theory
2014 mobile game
service, refunds were offered to customers who had bought items in-game or preordered the Vita port. The first hint of a localization appeared when the Agito
Final_Fantasy_Agito
Canadian politician (born 1973)
regarding the vaccine rollout plan and stated that Canada only focused on preordering vaccines from Pfizer and Moderna after a partnership with a Chinese company
Erin_O'Toole
Motor vehicle
gradually ramping up to 260,000 by 2028. In late 2019, with 10,000 units preordered, Sono predicted a September 2021 production start, with the preorder page
Sono_Motors_Sion
Category whose hom sets have algebraic structure
operation. If C is a closed monoidal category then C is enriched in itself. Preordered sets are categories enriched over a certain monoidal category, 2, consisting
Enriched_category
2021 as twenty-six hundred copies were preordered before public release. “Lớp Học Mật Ngữ” (literally means “Class of the Secret Language”) was a joint
Vietnamese_comics
Heart of Midlothian 2014–15 football season
of this change. The club's new home kit went on sale to people who had preordered on 15 May, priced at £45.00 for an adults top with kids priced at £35
2014–15 Heart of Midlothian F.C. season
2014–15_Heart_of_Midlothian_F.C._season
from a directed set to X {\displaystyle X} , where a directed set is a preordered set in which each finite subset has an upper bound. 2. A net x α {\displaystyle
Glossary of real and complex analysis
Glossary_of_real_and_complex_analysis
{\textstyle S} nonempty, because ∅ ∈ S {\textstyle \emptyset \in S} . It is preordered by A < B {\textstyle A<B} iff μ ( B − A ) = 0 {\textstyle \mu (B-A)=0}
Rokhlin_lemma
Structure in functional analysis
i\in \mathbb {N} } ), which is a net in X {\displaystyle X} since the preordered set ( I , ≤ ) {\displaystyle (I,\leq )} is directed (this preorder on
Complete topological vector space
Complete_topological_vector_space
Professional wrestling promotion
For Christmas in PR, Vázquez Ortega made a special offer for tickets preordered at his own business, Cobra Music Center. For Histeria Boricua 2009, IWA
International Wrestling Association (Puerto Rico)
International_Wrestling_Association_(Puerto_Rico)
Space with topology generated by convex sets
and only if every Cauchy net converges. A family of seminorms becomes a preordered set under the relation p α ≤ p β {\displaystyle p_{\alpha }\leq p_{\beta
Locally convex topological vector space
Locally_convex_topological_vector_space
Concept in probability
Troffaes, M.C.M., and S. Destercke (2011). Probability boxes on totally preordered spaces for multivariate modelling. International Journal of Approximate
Probability_box
travel, tourism, insurance
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travel, tourism, insurance