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Cofinite Topology

The double-pointed cofinite topology is the cofinite whose complement is the set A.

Cofinite Topology is described in multiple online sources, as addition to our editors' articles, see section below for printable documents, Cofinite Topology books and related discussion.

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PROFESSOR SMITH MATH 295 LECTURE NOTES 1. November 2
Nov 2, 2010 Another topology were all subsets are compact: The Cofinite Proof it is a topology: take {Uλ}λ∈Λ to be open sets in the cofinite topology on X.
Transversal and T1-independent topologies
generated by τ ∪ σ is discrete. Definition 2. Topologies τ,σ ⊆ P(X) are T1- independent whenever the topology τ ∧ σ = τ ∩ σ is the cofinite topology on X, i.
§2: THE NOTION OF A TOPOLOGICAL SPACE Part of the
Example (cofinite topology): Let X be an infinite set, and let τ consist of ∅ together with subsets whose complement is finite (or, for short, “cofinite subsets”).
2 SEPARATION AXIOMS
T2 is a product preserving topological property. Every T2 space is T1. Example 2.
Introduction to General Topology
called cofinite topology. ⊓⊔. Definition 1.

Suggested Web Resources

Cofiniteness - Wikipedia, the free encyclopedia
The cofinite topology (sometimes called the finite complement topology) is a topology which can be defined on every set X.
Cofinite Topology
PlanetMath: finite complement topology
Let $X$ be a set.
Cofinite Topology -- from Wolfram MathWorld
Aug 29, 2011 Number Theory · Probability and Statistics · Recreational Mathematics · Topology Topology > General Topology >.
Topology/Topological Spaces - Wikibooks, open books for an open
is a topology on X called the cofinite topology (or "finite complement topology") on X.

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