If $A$ is a Hausdorff space such that $A = \bigcup\limits_{i = 1}^\infty {{K_i}} $ where $K_i$ are its compact subsets, is $A$ a paracompact space? If not, what additional conditions should we add? (e.g. locally compact)
Conditions leading to paracompactness
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general-topology
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0Don't know off-hand, but adding regularity would suffice, since a countable union of compact sets is Lindelof, and regular+Lindelof implies paracompact. – 2011-12-08