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    Compactness of point and compact set product

    I get it now, thanks. Now, at the risk of seeming kind of stubborn, imagine you've just been given the definition of compact sets and you were immediately asked to prove this (which is the case with Spivak's book), how would you do it without constructing the functions \phi and \psi , which...
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    Compactness of point and compact set product

    While I don't doubt there's nothing wrong with your argument, I am not familiar with homeomorphisms and your proof seems a little out of my grasp right now. I am trying to prove it by means of covers, I suppose A is a cover of \{x\}\times B , and I want to prove there is a finite subcollection...
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    Compactness of point and compact set product

    I was reading Spivak's Calculus on Manifolds and in chapter 1, section 2, dealing with compactness of sets he mentions that it is "easy to see" that if B \subset R^m and x \in R^n then \{x\}\times B \subset R^{n+M} is compact. While it is certainly plausible, I can't quite get how to handle...
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    Self studying little Spivak's, stuck on problem 1-6

    ok ok ok I get it now, thank you very much ;D
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    Self studying little Spivak's, stuck on problem 1-6

    In an effort to keep me from spending all summer lying on the couch, I recently started reading Michael Spivak's Calculus on Manifolds; while working on problem 1-6 I got stuck on a technical detail and I was wondering if anyone could provide a little insight. Problem 1-6 says: Let f and g...
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