Recent content by rustyrake

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    Topology - prove that X has a countable base

    still don't get it... maybe it's too late. i'll think more about it in the morning. but: if i take only U's from those U\times V's... why isn't it already our base?
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    Topology - prove that X has a countable base

    :( i don't get it. why intersections? and... intersections of what? yes, but according to the definition of compactness i know, X is Hausdorff and i don't have to prove it.
  3. R

    Topology - prove that X has a countable base

    hm, ok, and i do this for each n, and get countable family of finite families of small open sets, and my base are all those small open sets? what do you mean?
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    Topology - prove that X has a countable base

    meaning: choose a finite number of them? and compactness of what?
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    Topology - prove that X has a countable base

    Homework Statement X - topological compact space \Delta = \{(x, y) \in X \times X: x=y \} \subset X \times X \Delta = \bigcap_{n=1}^{\infty} G_{n}, where G_{1}, G_{2}, ... \subset X \times X are open subsets. Show that the topology of X has a countable base. Homework Equations The Attempt...