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base-paracompact; strongly base-paracompact; partition of unity; Lindelöf spaces
A space $X$ is said to be {\it 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 $\Cal F$.
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