Abstract:A space $X$ is said to be {strongly base-paracompact} if there is a basis $\Cal B$ for $X$ with $|\Cal B|=w(X)$ such that every open cover of $X$ has a star-finite open refinement by members of $\Cal B$. Strongly paracompact spaces which are strongly base-paracompact are studied. Strongly base-paracompact spaces are shown have a family of functions $\Cal {F}$ with cardinality equal to the weight such that every open cover has a locally finite partition of unity subordinated to it from $\Cal F$.
Keywords: base-paracompact, strongly base-paracompact, partition of unity, Lindel\"of spaces
AMS Subject Classification: 54D20