# Article

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Keywords:
base-paracompact; strongly base-paracompact; partition of unity; Lindelöf spaces
Summary:
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 $\Cal F$.
References:
[E] Engelking R.: General Topology Heldermann Verlag, Berlin (1989). MR 1039321 | Zbl 0684.54001
[M] Morita K.: Normal families and dimension theory for metric spaces. Math. Ann. 128 (1954), 350-362. MR 0065906 | Zbl 0057.39001
[N] Nagata J.: On imbedding theorem for non-separable metric spaces. J. Inst. Polyt. Oasaka City Univ. 8 (1957), 128-130. Zbl 0079.38802
[Ny] Nyikos P.J.: Some surprising base properties in topology II. Set-theoretic Topology Papers, Inst. Medicine and Math., Ohio University, Athens Ohio, 1975-1976 Academic Press, New York (1977), 277-305. MR 0442889 | Zbl 0397.54004
[P] Ponomarev V.I.: On the invariance of strong paracompactness under open perfect mappings. Bull. Acad. Pol. Sci. Sér. Math. 10 (1962), 425-428. MR 0142107
Porter J.E.: Base-paracompact spaces. to appear in Topology Appl. MR 1956610 | Zbl 1099.54021

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