Difference between revisions of "Cofinite subset"
From Encyclopedia of Mathematics
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The family \mathcal{F}(X) of cofinite subsets of X forms a [[filter]], known as the '''Fréchet filter''' on X. It is contained in any non-principal ultrafilter on X. | The family \mathcal{F}(X) of cofinite subsets of X forms a [[filter]], known as the '''Fréchet filter''' on X. It is contained in any non-principal ultrafilter on X. | ||
| − | The cofinite subsets of X, together with the empty set, constitute the open sets of a [[topology]] on X, known as the '''cofinite topology'''. | + | The cofinite subsets of X, together with the empty set, constitute the open sets of a [[Topological structure (topology)|topology]] on X, known as the '''cofinite topology'''. |
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Revision as of 10:07, 22 October 2016
of a set X
A subset A of X for which the relative complement X \setminus A is finite.
The family \mathcal{F}(X) of cofinite subsets of X forms a filter, known as the Fréchet filter on X. It is contained in any non-principal ultrafilter on X.
The cofinite subsets of X, together with the empty set, constitute the open sets of a topology on X, known as the cofinite topology.
How to Cite This Entry:
Cofinite subset. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Cofinite_subset&oldid=39478
Cofinite subset. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Cofinite_subset&oldid=39478