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Notes on characterization of paracompact frames. (English) Zbl 0672.54018

Summary: A proof of several characteristics of paracompactness in the general localic setting using a procedure very similar to the classical one is presented. Among these, the characterizations concerning full normality and \(\sigma\)-local finiteness have been proved by other techniques before; we add characterizations by the existence of locally finite quasirefinements, and of \(\sigma\)-discrete refinements.

MSC:

54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
06D99 Distributive lattices
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