|Dec14-11, 12:16 AM||#1|
cauchy sequences and continuity versus uniform continuity
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.
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