11.12.2012 23:46, quasi wrote: > 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.