η-compact

Definition

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

• cf. realcompact.

Reference

• M.Mandelker, Supports of Continuous Functions, Trans. Amer. Math. Soc., 156 (1971), 73-83.
• http://www.utm.edu/staff/jschomme/weakdefs.html