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rustyrake
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Homework Statement
[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.
Homework Equations
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...