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Directed set


In mathematics, a directed set is a nonempty set A together with a reflexive and transitive binary relation ≤ (that is, a preorder), with the additional property that ...

Directed sets - nLab


Jun 22, 2014 ... A directed set is a set equipped with a direction. A directed poset is a directed set whose preorder is a partial order (so directed proset might be ...

Upward-directed set - Encyclopedia - The Free Dictionary

encyclopedia2.thefreedictionary.com/Upward-directed set

A partially ordered set with the property that for every pair of elements a,b in the set, there is a third element which is larger than both a and b. Also known as ...

lattice orders - supremum of directed set is contained or not ...


Oct 8, 2013 ... But I have also seen sets such as [ o , a ) used as examples of directed sets that do not contain their supremum. My sense is that finite directed ...

Chain-complete posets and directed sets with applications


sharpens the known result ([,8], [,181) that in any chain-complete poset, every directed set has a sup. Often a property holds for every directed set if and only if it  ...

directed sets and cofinal types - American Mathematical Society


directed sets of size S,, but that there exist many cofinal types of directed sets of ... directed sets D and E are cofinally similar if there is a partially ordered set C in.

Directed Sets, Nets, Ideals, Filters, and Maps - Formalized ...


directed sets, nets, ideals, filters, and . . . 95. (6) Let L be a non empty transitive relational structure, S be a filtered- infs-inheriting non empty full relational ...

Topology/Lesson 5 - Wikiversity


May 29, 2015 ... Directed Sets[edit]. Directed sets are very useful in topology. We will explore a couple of their uses in this lesson.

Nets and Filters


Proposition 5 A filter U is maximal if and only if every set A that inter- sects every ... Definition 1 A directed set is a set D with a relation ≤ on it satisfying. 1.

Directed Sets and Cofinal Types - JStor


directed sets of size Sl, but that there exist many cofinal types of directed sets of ... directed sets D and E are cofinally similar if there is a partially ordered set C in.

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Directed Set -- from Wolfram MathWorld


Directed Set. A set S together with a relation >= which is both transitive and reflexive such that for any two elements a,b in S , there exists another element c in S ...

directed set | planetmath.org


Aug 1, 2002 ... A directed set is a partially ordered set ( A ) A (A,\leq) such that whenever a , b ∈ A a b A a,b\in A there is an x ∈ A x A x\in A such that a ≤ x a x ...

1 Directed sets and nets


Apr 22, 2009 ... book. 1 Directed sets and nets. We first recall some basic definitions. Definition 1.1. We say that (D, ≤) is a directed set, if ≤ is a relation on D.