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Homework Help: Cauchy sequences and continuity versus uniform continuity

  1. Dec 14, 2011 #1
    1. The problem statement, all variables and given/known data

    This isn't really a problem but it is just something I am curious about, I found a theorem stating that you have two metric spaces and f:X --> Y is uniform continuous and (xn) is a cauchy sequence in X then f(xn) is a cauchy sequence in Y.

    2. Relevant equations

    This proposition is for uniform continuity but I am wondering if it also holds true for just regular continuity.
  2. jcsd
  3. Dec 14, 2011 #2


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    Staff Emeritus
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    Think about f(x)=1/x
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