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η-compact

Last-modified: 2010-12-28 (火) 21:48:15

Definition Edit

Let X be a Tychonoff space.
We let C(X) be the ring of all continuous functions on X, C_ψ(X) the ring of all continuous functions with pseudocompact support, I(X) the the intersection of all free maximal ideals of C(X).
We say X is η-compact iff C_ψ(X) = I(X).

Remark Edit

Reference Edit