Base-cover paracompactness
Strashimir G. Popvassilev · Proceedings of the American Mathematical Society · 2004
Call a topological space X X base - cover paracompact if X X has an open base B \mathcal {B} such that every cover C ⊂ B \mathcal {C}\subset \mathcal {B} of X X contains a locally finite subcover. A subspace of the Sorgenfrey line is base-cover paracompact if and only if it is F σ F_\sigma . The countable sequential fan is not base-cover paracompact. A paracompact space is locally compact if and only if its product with every compact space is base-cover paracompact.