strongly compact

strongly compact

Definition

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

Property

• [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

• 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.