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cofinite and cocountable topologies∗
yark†
2013-03-21 14:54:24
The cofinite topology on a set X is defined to be the topology T where
T = {A ⊆ X | X \ A is finite, or A = ∅}.
In other words, the closed sets in the cofinite topology are X and the finite
subsets of X.
Analogously, the cocountable topology on X is defined to be the topology in
which the closed sets are X and the countable subsets of X.
The cofinite topology on X is the coarsest T1 topology on X.
The cofinite topology on a finite set X is the discrete topology. Similarly,
the cocountable topology on a countable set X is the discrete topology.
A set X together with the cofinite topology forms a compact topological
space.
∗ hCofiniteAndCocountableTopologiesi created: h2013-03-21i by: hyarki version: h33464i
Privacy setting: h1i hDefinitioni h54B99i
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