Displaying similar documents to “Base-base paracompactness and subsets of the Sorgenfrey line”

Strongly base-paracompact spaces

John E. Porter (2003)

Commentationes Mathematicae Universitatis Carolinae

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A space X is said to be if there is a basis ℬ for X with | ℬ | = w ( X ) such that every open cover of X has a star-finite open refinement by members of ℬ . Strongly paracompact spaces which are strongly base-paracompact are studied. Strongly base-paracompact spaces are shown have a family of functions ℱ with cardinality equal to the weight such that every open cover has a locally finite partition of unity subordinated to it from ℱ .

Some versions of relative paracompactness and their absolute embeddings

Shinji Kawaguchi (2007)

Commentationes Mathematicae Universitatis Carolinae

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Arhangel’skii [Sci. Math. Jpn. 55 (2002), 153–201] defined notions of relative paracompactness in terms of locally finite open partial refinement and asked if one can generalize the notions above to the well known Michael’s criteria of paracompactness in [17] and [18]. In this paper, we consider some versions of relative paracompactness defined by locally finite (not necessarily open) partial refinement or locally finite closed partial refinement, and also consider closure-preserving...