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n-starcompact

Last-modified: 2015-12-24 (木) 21:55:24

Definition Edit

A space X is said to be n-starcompact if for every open cover U of X, there is some finite subset V of U such that imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20st%5en%28%5ccup%5cmathcal%7bV%7d%2c%5cmathcal%7bU%7d%29=X%20%5c%5d%7d%25.png, where if B is subset of X and H is collection of subsets of X, imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20st%5en%28B%2c%5cmathcal%7bH%7d%29=%5ccup%20ST%5en%28B%2c%5cmathcal%7bH%7d%29%20%5c%5d%7d%25.png , imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20St%5en%28B%2c%5cmathcal%7bH%7d%29=%5c%7bH%5cin%5cmathcal%7bH%7d;H%5ccap%20st%5e%7bn-1%7d%28B%2c%5cmathcal%7bH%7d%29%5cneq%5cemptyset%5c%7d%20%5c%5d%7d%25.png, imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20st%5e1%28B%2c%5cmathcal%7bH%7d%29=%5ccup%20ST%5e1%28B%2c%5cmathcal%7bH%7d%29%20%5c%5d%7d%25.png, imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20St%5e1%28B%2c%5cmathcal%7bH%7d%29=%5c%7bH%5cin%5cmathcal%7bH%7d;H%5ccap%20B%5cneq%5cemptyset%5c%7d%20%5c%5d%7d%25.png.

Reference Edit

  • van Douwen, E. K., Reed, G. M.(4-OXSE), Roscoe, A. W.(4-OXUC) and Tree, I. J.(4-OXM),Star covering properties, Topology Appl. 39 (1991), no. 1, 71--103.