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strongly compact

Last-modified: 2010-08-24 (火) 17:49:42

strongly compact

Definition Edit

A topological space is called strongly compact iff every preopen cover has a finite subcover.

Property Edit

  • [Ganster1987] For a topological space X, the following are equivalent
    1. X is strongly compact
    2. X is compact and every infinite subset of X has a nonempty interior.
    3. X is quasi H-closed and every infinite subset of X has a nonempty interior.
  • [Ganster1987] The 1?point?compactification of any discrete space is strongly compact.

Reference Edit

  • J. Dontchev, M. Ganster and T. Noiri, On p-closed spaces, Internat. J. Math. & Math. Sci. Vol.24, No.3 (2000) pp.203-212.
  • M. Ganster, Some remarks on strongly compact spaces and semi compact spaces, Bull. Malaysian Math. Soc. (10) 2 (1987) pp.67-81.