Base-cover paracompactness

Abstract

Abstract. Call a topological space X base-cover paracompact if X has an open base B such that every cover C ⊂ B of X contains a locally finite subcover. A subspace of the Sorgenfrey line is base-cover paracompact if and only if it is Fσ. 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.