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is equivalent to saying that the preordered set is the opposite of a closed preordered set. Inductive preordered sets satisfy Zorn's lemma and the Bourbaki–Witt
Closed_preordered_set
Subset of a preorder that contains all larger elements
complex - a set-family that is downwards-closed with respect to the containment relation. Given an element x {\displaystyle x} of a preordered set ( X , ≤
Upper_and_lower_sets
Class equipped with a preorder
These concepts generalize respectively those of preordered set, partially ordered set and totally ordered set. However, it is difficult to work with them
Preordered_class
Mathematical set with an ordering
terminal object. Also, every preordered set is equivalent to a poset. Finally, every subcategory of a poset is isomorphism-closed. If P {\displaystyle P} is
Partially_ordered_set
All numbers between two given numbers
defined in arbitrary partially ordered sets or more generally, in arbitrary preordered sets. For a preordered set ( X , ≲ ) {\displaystyle (X,\lesssim )}
Interval_(mathematics)
topology if and only if it is upward-closed. Let ( X , ≲ ) {\displaystyle (X,\lesssim )} be a closed preordered set (one in which every chain has an upper
Saturated set (intersection of open sets)
Saturated_set_(intersection_of_open_sets)
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
Mathematical ordering with upper bounds
In mathematics, a directed set (or a directed preorder or a filtered set) is a preordered set in which every finite subset has an upper bound. In other
Directed_set
Category where each homset contains at most one morphism
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 (i.e. whose
Thin_category
Vector space with a partial order
{\displaystyle \,\leq \,} on the set X , {\displaystyle X,} the pair ( X , ≤ ) {\displaystyle (X,\leq )} is called a preordered vector space and we say that
Ordered_vector_space
Algebraic concept in measure theory, also referred to as an algebra of sets
descriptions of redirect targets π-system – Family of sets closed under intersection Preordered field – Algebraic object with an ordered structurePages
Field_of_sets
Type of topology in mathematics
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
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
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 other
Maximal_and_minimal_elements
Function that returns cardinal numbers
null sets or the ideal of meagre sets, these cardinal invariants are referred to as cardinal characteristics of the continuum. For a preordered set ( P
Cardinal_function
Partially ordered vector space, ordered as a lattice
{\displaystyle a\leq b} (resp. a ≥ b {\displaystyle a\geq b} ). A preordered vector lattice is a preordered vector space E {\displaystyle E} in which every pair of
Riesz_space
Mathematical object that generalizes the standard notions of sets and functions
{\displaystyle I} as objects and only the identity morphisms as morphisms. Any preordered set ( P , ≤ ) {\displaystyle (P,\leq )} forms a small category, where the
Category_(mathematics)
Mathematical concept
set is open in X. So for finite spaces, the topology on X is uniquely determined by ≤. Going in the other direction, suppose (X, ≤) is a preordered set
Finite_topological_space
Algebraic structure
frames corresponding to interior algebras are precisely the preordered sets. Preordered sets (also called S4-frames) provide the Kripke semantics of the
Interior_algebra
functor has a left adjoint, which places the Alexandrov topology on a preordered set. There are spaces that are more specific than T0 spaces for which this
Specialization_preorder
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
Special subset of a partially ordered set
closure of S (i.e., the smallest upwards-closed set containing S) is equal to F. Since every filter is upwards-closed, every filter is a base for itself. Moreover
Filter_(mathematics)
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
Precisely, a net on a set X {\displaystyle X} is a map from a directed set to X {\displaystyle X} , where a directed set is a preordered set in which each finite
Glossary of real and complex analysis
Glossary_of_real_and_complex_analysis
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
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
2016 play by Jack Thorne
"Definitive Collector's Edition". According to CNN, this was the most preordered book of 2016. In the United States and Canada, the book sold over 2 million
Harry Potter and the Cursed Child
Harry_Potter_and_the_Cursed_Child
Use of filters to describe and characterize all basic topological notions and results
infrequent). A map h : A → I {\displaystyle h:A\to I} between two preordered sets is order-preserving if whenever a , b ∈ A {\displaystyle a,b\in A}
Filters_in_topology
Mathematical proposition equivalent to the axiom of 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 a
Zorn's_lemma
Theorem in economics
semi-normally-preordered topological space. If X is a locally compact and sigma-compact Hausdorff space, and ⪰ {\displaystyle \succeq } is a closed subset of
Utility representation theorem
Utility_representation_theorem
Branch of mathematics
finite subsets, but 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
Order_theory
Space with topology generated by convex sets
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
Handheld game console
on February 4, 2022. Retrieved February 4, 2022. "3DS Amazon UK's most preordered system ever". GameSpot. March 17, 2011. Archived from the original on
Nintendo_3DS
2025 extraction shooter video game
stage on 28 December 2016, which would be available to select users who preordered the game. This was the stage where Battlestate released the game in four
Escape_from_Tarkov
Overview of and topical guide to category theory
Hilbert spaces Category of sets and relations Category of topological spaces Category of metric spaces Category of preordered sets Category of groups Category
Outline_of_category_theory
2003 video game
Rebellion was distributed in a first come first served basis to people who preordered Devil May Cry 2 through participating retailers. The South Korea-exclusive
Devil_May_Cry_2
Vector space with a binary relation
{\displaystyle x=0.} A preordered vector space ( X , ≤ ) {\displaystyle (X,\leq )} with an order unit u {\displaystyle u} is Archimedean preordered if and only if
Archimedean ordered vector space
Archimedean_ordered_vector_space
Category whose hom sets have algebraic structure
product as the monoidal operation. If C is a closed monoidal category then C is enriched in itself. Preordered sets are categories enriched over a certain monoidal
Enriched_category
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
Algebraic structure with an associative operation and an identity element
since the identity elements may differ. For example, the singleton set {0} is closed under multiplication, and is not a submonoid of the (multiplicative)
Monoid
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
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)
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
Transformation of one computational problem to another
reduction. Reducibility is a preordering, that is, a reflexive and transitive relation, on P(N)×P(N), where P(N) is the power set of the natural numbers. As
Reduction_(complexity)
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
2008 video game
Zero Wing and the internet meme of the same name. Red Alert 3 could be preordered and contained bonuses including the Command & Conquer: Red Alert 2 game
Command & Conquer: Red Alert 3
Command_&_Conquer:_Red_Alert_3
2010 video game
upcoming installment in the Ghost Recon series, as well as people who preordered the game from GameStop or PlayStation Plus members. On April 13, 2010
Tom Clancy's Splinter Cell: Conviction
Tom_Clancy's_Splinter_Cell:_Conviction
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
2018 2.5D Dragon Ball fighting game
Joy-Con controller play in single-player and multiplayer modes. Players who preordered Dragon Ball FighterZ on console received early access to the game's open
Dragon_Ball_FighterZ
American infrastructure and tunneling company
testing. In 2018, the company began offering 20,000 "flamethrowers" for preordering. The "flamethrower" was a blow torch shaped to look like a gun and is
The_Boring_Company
{\textstyle <\epsilon } . The set S {\textstyle S} nonempty, because ∅ ∈ S {\textstyle \emptyset \in S} . It is preordered by A < B {\textstyle A<B} iff
Rokhlin_lemma
Home video game console
website instead, with the release delayed to February 2021 for those who preordered in 2018 and 2019. The consoles were assembled in Myanmar, where protests
Polymega
American bicycle manufacturer
wide with riders having to sign up to pre-order the bike. Those that preordered the bike had the opportunity to have their signature etched onto the bike
Dahon
2011 video game
Also announced at that time were three pre-order bonuses; players who preordered the game at Amazon would get a prequel comic, those who used Best Buy
F.E.A.R._3
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
2011 video game
the Massassi. Shadow of Revan was available for preorder. Players who preordered before November 2, 2014, received an experience boost that granted twelve
Star_Wars:_The_Old_Republic
Contagious disease caused by 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
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
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
2011 video game remaster
Microsoft's annual E3 global media briefing, which closed with the teaser trailer for Halo 4. Bonuses for preordering the game included a Master Chief Xbox 360
Halo: Combat Evolved Anniversary
Halo:_Combat_Evolved_Anniversary
Video game series
with a limited steel box edition of Project Origin available only by preordering the game from GameStop, Armacham Field Guide is a primer detailing much
F.E.A.R.
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 I
Complete topological vector space
Complete_topological_vector_space
Spanish smartphone company
a slight improvement from the Peak+ model. The customers who already preordered and paid for the unreleased Peak+ model were offered to get a Revolution
GeeksPhone
2010 music video game
"My Own Summer" by Deftones, and "Blue Monday" by New Order. Players preordering the game through Amazon.com or Best Buy received immediate access to
Rock_Band_3
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
CLOSED PREORDERED-SET
CLOSED PREORDERED-SET
Surname or Lastname
English
English : variant spelling of Close.Americanized spelling of German Klaus.
Male
English
Anglicized form of Hebrew Kesed, CHESED means "increase." In the bible, this is the name of the 4th son of Nahor.
Biblical
as a devil, or a destroyer
Girl/Female
American, Anglo, Australian, British, Christian, English, Jamaican, Portuguese
Clover; Flower Name; Fortunate; Mind; Heart; Spirit
Girl/Female
Tamil
Nimeelitha | நீமிலீதா
Closed
Nimeelitha | நீமிலீதா
Female
English
Old English flower name, CLOVER means simply "clover."
Surname or Lastname
English
English : topographic name for someone who lived by an enclosure of some sort, such as a courtyard set back from the main street or a farmyard, from Middle English clos(e) (Old French clos, from Late Latin clausum, past participle of claudere ‘to close’).English : from Middle English clos(e) ‘secret’, applied as a nickname for a reserved or secretive person.Dutch : variant of Claeys.Altered spelling of German Klose.
Girl/Female
Hindu
Closed
Surname or Lastname
English
English : variant of Close 1.German : variant of Kloss.
Girl/Female
Anglo Saxon English
Clover.
Boy/Male
Hindu, Indian
Cloud; Grain Cooked with Milk
Surname or Lastname
English
English : occupational name for a nailer, from an agent derivative of Old French clou ‘nail’. Compare Cloutier.Americanized spelling of German Klauer (or the variant Clauer) or of Glauer, a nickname from Middle High German glau, glou ‘intelligent’, ‘circumspect’.
Boy/Male
Biblical
As a devil or a destroyer.
Surname or Lastname
English
English : Devon variant of Clough.
Surname or Lastname
English
English : variant spelling Clow.
Surname or Lastname
English
English : topographic name for someone who lived near an outcrop or hill, from Old English clÅ«d ‘rock’ (only later used to denote vapor formations in the sky).French : from the Germanic personal name Hlodald, composed of the elements hlÅd ‘famous’, ‘clear’ + wald ‘rule’, which was borne by a saint and bishop of the 6th century.
Surname or Lastname
English
English : variant of Cleaver.
Boy/Male
Australian, Biblical, Christian
Destroyer
Boy/Male
Shakespearean
Cymbeline' The Queen's son by a former husband.
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Tamil, Telugu
Close; Clove
CLOSED PREORDERED-SET
CLOSED PREORDERED-SET
Girl/Female
Hindu, Indian
Nature
Girl/Female
Hindu
Union
Boy/Male
Hindu
Person having all qualities
Boy/Male
Hindu
Defender of the oppressed
Boy/Male
Arabic, Indian, Muslim, Sindhi
Glory of the Faith; Emperor; Pride of Religion
Male
Egyptian
, the father of officer Se-uati.
Male
Dutch
, resolute helmet.
Girl/Female
Bengali, Hindu, Indian, Kannada, Malayalam, Marathi
Whole
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : of much disputed origin, but probably from a Germanic personal name composed of the elements tal ‘destroy’ + bod ‘message’, ‘tidings’, i.e. ‘messenger of destruction’. In this form the name is also found in France, taken there apparently by English immigrants; the usual French form is Talbert.Talbot is the name of an ancient Irish family of Norman origin, which have held the earldoms of Shrewsbury and Waterford since the 15th century. They were granted the baronial estate of Malahide, near Dublin, by Henry II (1154–89), an estate that they held for over 850 years. They trace their descent from Richard de Talbott, mentioned in the Domesday Book. His son, Hugh de Talbot or Talebot’h, became governor of Plessis Castle, Normandy, France, in 1118.
Boy/Male
Hindu
King of gods, Lord Indra
CLOSED PREORDERED-SET
CLOSED PREORDERED-SET
CLOSED PREORDERED-SET
CLOSED PREORDERED-SET
CLOSED PREORDERED-SET
v. i.
To end, terminate, or come to a period; as, the debate closed at six o'clock.
v. t.
Short; as, to cut grass or hair close.
v. t.
To shut up in, or as in, a closet; to conceal.
v. t.
To make into a closet for a secret interview.
adv.
In a close manner.
v. t.
Difficult to obtain; as, money is close.
n.
One who, or that which, closes; specifically, a boot closer. See under Boot.
imp. & p. p.
of Close
n.
To stop, or fill up, as an opening; to shut; as, to close the eyes; to close a door.
a.
Firmly barred or closed.
v. t.
Concise; to the point; as, close reasoning.
v. t.
Nearly equal; almost evenly balanced; as, a close vote.
adv.
In a close manner.
v. t.
To make close.
v. t.
Narrow; confined; as, a close alley; close quarters.
v. t.
Strictly confined; carefully quarded; as, a close prisoner.
v. t.
Shut fast; closed; tight; as, a close box.
adv.
Close; closely.
superl.
Tight; close; closely fitting.
pl.
of Couple-close