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ψ-compact

Last-modified: 2010-12-28 (火) 21:37:51

Definition Edit

Let X be a Tychonoff space.
Let C_K(X) denote the collection of continuous functions with compact support, C_Ψ(X) the collection of continuous functions with pseudocompact support.
X is called Ψ-compact if C_K(X)=C_Ψ(X).

Remark Edit

cf. realcompact.

Reference Edit

John J. Schommer and Mary Anne Swardson, Almost* realcompactness, Commentationes Mathematicae Universitatis Carolinae, Vol.42 (2001), No.2, 383-392.