Subject: metric spaces From: "Michael Cole" Date: Thu, 23 Mar 2006 16:06:53 -0500 Dear Colleagues, I have an elementary question. It seems to me that there should exist a theorem along the following lines: If X is metrizable and locally compact and satisfies some countability condition and perhaps other hypotheses, then there exists a metric for X with respect to which any closed and bounded set is compact. I am assuming that this question is old hat and the necessary hypotheses are known. What are the necessary hypotheses? Michael Cole