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G_δ-relatively realcompact

Last-modified: 2015-11-19 (木) 14:35:10

imgtex.fcgi?%5bres=100%5d%7b$G_%5cdelta$%7d%25.png-relatively realcompact

Definition Edit

A subset A of a topological space X is called imgtex.fcgi?%5bres=100%5d%7b$G_%5cdelta$%7d%25.png-relatively realcompact in X iff imgtex.fcgi?%5bres=100%5d%7b$G_%5cdelta%5ctext%7b-cl%7d_%7b%5cnu%20X%7dA%5csubset%20X$%7d%25.png, where imgtex.fcgi?%5bres=100%5d%7b$G_%5cdelta%5ctext%7b-cl%7d_%7b%5cnu%20X%7dA$%7d%25.png denotes the set of all points p such that whenever G is a imgtex.fcgi?%5bres=100%5d%7b$G_%5cdelta$%7d%25.png-set containing p, G meets A, called the imgtex.fcgi?%5bres=100%5d%7b$G_%5cdelta$%7d%25.png-closure of A in imgtex.fcgi?%5bres=100%5d%7b$%5cnu%20X$%7d%25.png.

Remark Edit

Reference Edit

  • J. J. Shommer, Relatively realcompact sets and nearly pseudocompact spaces, Comment. Math. Univ. Calorin. 34,2 (1993) 375-382.