cauchy sequences and continuity versus uniform continuity

renjean

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.

Office_Shredder

Think about f(x)=1/x