Cocountable topology
id:
cocountable-topology-275-16652809
title:
Cocountable topology
text:
The cocountable topology or countable complement topology on any set X consists of the empty set and all cocountable subsets of X, that is all sets whose complement in X is countable. It follows that the only closed subsets are X and the countable subsets of X. Symbolically, one writes the topology as Every set X with the cocountable topology is Lindelöf, since every nonempty open set omits only countably many points of X. It is also T1, as all singletons are closed. If X is an uncountable set t
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wiki
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encyclopedia
description:
original url:
https://en.wikipedia.org/wiki/Cocountable_topology
date created:
date modified:
2023-07-28T16:35:52Z
main entity:
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13
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