quasi
Posts:
12,021
Registered:
7/15/05


Re: Precompactness
Posted:
Dec 11, 2012 4:46 PM


Virgil wrote: >Kaba wrote: >> >> Let X be a locally compact Hausdorff space. Is every open >> set of X precompact (compact closure)? > >Isn't the whole space, X, an open set with a not necessarily >compact closure, at least if X is only locally compact?
Yes.
Also, for all positive integers n, R^n is locally compact, but any unbounded open set is not precomnpact.
quasi

