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