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Intersections of minimal prime ideals in the rings of continuous functions

Swapan Kumar Ghosh (2006)

Commentationes Mathematicae Universitatis Carolinae

A space X is called μ -compact by M. Mandelker if the intersection of all free maximal ideals of C ( X ) coincides with the ring C K ( X ) of all functions in C ( X ) with compact support. In this paper we introduce φ -compact and φ ' -compact spaces and we show that a space is μ -compact if and only if it is both φ -compact and φ ' -compact. We also establish that every space X admits a φ -compactification and a φ ' -compactification. Examples and counterexamples are given.

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