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Last-modified: 2010-12-17 (金) 22:45:46

Definition Edit

A T_1 space X is called superparacompact if every open cover has an open finite component refinement.

Property Edit

Let X be a completely regular space and let imgtex.fcgi?%5bres=100%5d%7b$%5cbeta%20X$%7d%25.png be its Stone-Cech compactification. X is superparacompact iff for every compact imgtex.fcgi?%5bres=100%5d%7b$B%5csubset%5cbeta%20X%5csetminus%20X$%7d%25.png, there exists a finite component cover imgtex.fcgi?%5bres=100%5d%7b$%5cmathcal%7bV%7d$%7d%25.png of the space X such that imgtex.fcgi?%5bres=100%5d%7b$B%5ccap%20%28%5ccup%5c%7b%20%5bW%5d_%7b%5cbeta%20X%7d:W%5cin%20%5cmathcal%7bV%7d%5c%7d%20=%5cemptyset%29$%7d%25.png, where imgtex.fcgi?%5bres=100%5d%7b$%5bW%5d_%7b%5cbeta%20X%7d$%7d%25.png denotes the closure of W in imgtex.fcgi?%5bres=100%5d%7b$%5cbeta%20X$%7d%25.png.

Reference Edit

  • D. Buhagiar and T. Miwa, On superparacompact and Lindeloef GO-spaces, Houston J. Math. Vol.24, No.3, 1998.
  • D. Buhagiar, T. Miwa, and B. A. Pasynkov, Superparacompact type properties, Yokohama Math. J. Vol.46, pp.71-86, 1998.