Must a Hausdorff Baire space be $σ-$compact?
A Baire space is a topological space in which the union of every countable collection of closed sets with empty interior has empty interior.
A topological space X is called $σ-$compact if it is the countable union of compact subsets.
Just now, from the http://en.wikipedia.org/wiki/Σ-compact_space, I found that conclusion as follows:
A Hausdorff, Baire space that is also σ-compact, must be locally compact at at least one point.
How to prove it?
Thanks a lot.