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## Directed set

en.wikipedia.org/wiki/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

ncatlab.org/nlab/show/direction

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 ...

## directed set | planetmath.org

planetmath.org/directedset

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

thales.doa.fmph.uniba.sk/sleziak/texty/rozne/topo/subnets2.pdf

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.

## directed sets and cofinal types - American Mathematical Society

www.ams.org/tran/1985-290-02/S0002-9947-1985-0792822-9/S0002-9947-1985-0792822-9.pdf

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.

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

math.stackexchange.com/questions/519576/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 ...

## general topology - Example of directed set (directed towards \$x_0 ...

math.stackexchange.com/questions/135523/example-of-directed-set-directed-towards-x-0

Apr 22, 2012 ... We then say that the reals have been directed towards x 0 . This is an example of a directed set that is not ordered (neither totally nor partially)." ...

## general topology - Can directed set be finite? - Mathematics Stack ...

math.stackexchange.com/questions/446685/can-directed-set-be-finite

Jul 18, 2013 ... Note that in a directed set every finite subset has an upper bound. If the directed set itself is finite, then it must have a maximum (why?).

## elementary set theory - What are the key differences between a ...

math.stackexchange.com/questions/715164/what-are-the-key-differences-between-a-partially-ordered-set-and-a-filtered-fami

Mar 17, 2014 ... ... differences between a partially ordered set and a filtered family(directed) set? ... Partial order means the set has a "sequencing" and a "binary ...

## Topology/Lesson 5 - Wikiversity

en.wikiversity.org/wiki/Topology/Lesson_5

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

### Directed Set -- from Wolfram MathWorld

mathworld.wolfram.com

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 ...

### Upward-directed set - Encyclopedia - The Free Dictionary

encyclopedia2.thefreedictionary.com

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 ...

### Directed set - Encyclopedia of Mathematics

www.encyclopediaofmath.org

Oct 14, 2014 ... A set A equipped with a directed order. A set A with partial order ≤ is called upwards (respectively, downwards) directed if ≤ (respectively, the ...