Topology #21 Axioms Of Countability

First countable and second countable topological spaces

[@Zxv975]

The empty set isn't in your last example, so if wouldn't he a topology, right?

[@aback93]

I think you are right, when you define the finite complement topology you have to state that it consists of the empty set and all subsets for which the complement is finite.

[@jonathangallagher3402]

You mean {U < R | R \ U is finite} |_| { R }.