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pointwise star-orthocompact

Last-modified: 2011-01-05 (水) 18:07:26

Definition Edit

A topological space X is called pointwise star-orthocompact if for every open cover imgtex.fcgi?%5bres=100%5d%7b$%5cmathcal%7bU%7d$%7d%25.png of
X, there exists an open Q-collection imgtex.fcgi?%5bres=100%5d%7b$%5cmathcal%7bV%7d=%5c%7bV_x:x%5cin%20X%5c%7d$%7d%25.png such that imgtex.fcgi?%5bres=100%5d%7b$x%5cin%20V_x%5csubset%20%5cmathrm%7bSt%7d%28x%2c%5cmathcal%7bU%7d%29$%7d%25.png.
Here, a collection U of open subsets is called Q-collection if for every subcollection V of U, imgtex.fcgi?%5bres=100%5d%7b$%5ccap%5cmathcal%7bV%7d$%7d%25.png is open.

Reference Edit

  • Gary Gruenhage, On closed images of orthocompact spaces, Proc. Amer. Math. Soc. Vol.77, No.3, pp.389-394 (1979)