I need an example for a compact, Hausdorff, separable space which is not first-countable. I tried to look for it for some time without success…

In an exercise from Munkres-Topology Article 30 the author writes that there is a very familiar space which is NOT first countable but every point is a $G_\delta $ set. What is it? Though there are answers posted on this site to the above question, I don’t find the spaces familiar to what has been […]

In topological space, does first countable+ separable imply second countable? If not, any counterexample?

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