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Spaces X In Which All Prime Z-Ideals Of C(X) Are Minimal Or Maximal, Melvin Henriksen, Jorge Martinez, R. G. Woods

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Quasi P-spaces are defined to be those Tychonoff spaces X such that each prime z-ideal of C(X) is either minimal or maximal. This article is devoted to a systematic study of these spaces, which are an obvious generalization of P-spaces. The compact quasi P-spaces are characterized as the compact spaces which are scattered and of Cantor-Bendixson index no greater than 2. A thorough account of locally compact quasi P-spaces is given. If X is a cozero-complemented space and every nowhere dense zeroset is a z-embedded P-space, then X is a quasi P-space. Conversely, if X is a quasi P-space and …