(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Give an example of two metric spaces (X_{1}, d_{1}) and (X_{2}, d_{2}) which are topologically equivalent and for which (X_{1}, d_{1}) is complete and (X_{2}, d_{2}) is not.

2. The attempt at a solution

The open unit disc and R^{2}. They are homeomorphic, but there are Cauchy sequences in the disc which will converge to limits outside of the disc, so it's not complete.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Metric spaces - is my answer right?

**Physics Forums | Science Articles, Homework Help, Discussion**