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mrbohn1
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Homework Statement
(a) Prove that R, with the cocountable topology, is not first countable.
(b) Find a subset A of R (with the cocountable topology), and a point z in the closure of A such that no sequence in A converges to z.
Homework Equations
(The cocountable topology on R has as its closed sets all the finite and countable subsets of R).
The Attempt at a Solution
I'm not really sure how to prove this. I know that if I could find a set and point meeting the conditions in part (b), then that would prove part (a), as in a first countable space X a point x belongs to the closure of a subset A of that space if and only if there is a sequence of points of A converging to x. However, I assume that I am expected to prove that R is not first countable with this topology some other way for part (a).
Either way, I'm stuck!
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