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Is R with the cofinite topo1o separable? Prove your answer.
Solution
Theorem:
Let T=(S,?) be a finite complement topology on an infinite set S.
Then T is a separable space.
Proof:
Let S be a set.
Then S is countably infinite iff there is a bijection f:S?N, where N is the set of natural numbers.
That is, it is an infinite set of the form:
{s0,s1,

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Is R with the cofinite topo1o separable Prove your answer. Solut.pdf

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