(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[itex]X[/itex] - topological compact space

[itex]\Delta = \{(x, y) \in X \times X: x=y \} \subset X \times X[/itex]

[itex]\Delta = \bigcap_{n=1}^{\infty} G_{n}[/itex], where [itex]G_{1}, G_{2}, ... \subset X \times X[/itex] are open subsets.

Show that the topology of [itex]X[/itex] has a countable base.

2. Relevant equations

3. The attempt at a solution

i have no idea what to start with. i don't really want to get a solution, just some clues...

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# Topology - prove that X has a countable base

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