A topological space is called $\sigma$-compact if it is a countable union of compact sets.
2026-02-23 04:43:00.1771821780
A topological space $(X, \tau)$ which is: $\sigma-$ compact, Hausdorff, and locally compact. Then X is also paracompact.
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HINT: A $\sigma$-compact space is easily shown to be Lindelöf, and a locally compact Hausdorff space is regular. Finally, regular Lindelöf spaces are paracompact.