Suppose that A is a subset of a metric space X. Does compactness of A depend on which metric is given to X? For example, if d(x,y) and p(x,y) are two possible metrics for X, is A compact with respect to the metric d(x,y) if and only if A is compact with respect to the metric p(x,y)?(adsbygoogle = window.adsbygoogle || []).push({});

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

Dismiss Notice

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!

# Compactness in metric spaces.

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