Displaying similar documents to “Paracompact and countably paracompact subsets”

Uniformization and anti-uniformization properties of ladder systems

Todd Eisworth, Gary Gruenhage, Oleg Pavlov, Paul Szeptycki (2004)

Fundamenta Mathematicae

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Natural weakenings of uniformizability of a ladder system on ω₁ are considered. It is shown that even assuming CH all the properties may be distinct in a strong sense. In addition, these properties are studied in conjunction with other properties inconsistent with full uniformizability, which we call anti-uniformization properties. The most important conjunction considered is the uniformization property we call countable metacompactness and the anti-uniformization property we call thinness....

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...