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super countably paracompact

Last-modified: 2010-12-17 (金) 22:26:26

Definition Edit

A topological space is said to be super countably paracompact iff. for every decreasing sequence of closed sets imgtex.fcgi?%5bres=100%5d%7b$F_n$%7d%25.png with an empty intersection, there is a decreasing sequence of cozero sets imgtex.fcgi?%5bres=100%5d%7b$P_n$%7d%25.png with imgtex.fcgi?%5bres=100%5d%7b$F_n%5csubset%20P_n$%7d%25.png and imgtex.fcgi?%5bres=100%5d%7b$%5cmathrm%7bcl%7dP_n$%7d%25.png have an empty intersection.

Reference Edit

John J. Schommer and Mary Anne Swardson, Almost realcompactness, Commentationes Mathematicae Universitatis Carolinae, Vol. 42 (2001), No. 2, 383–392.