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On nonregular ideals and z -ideals in C ( X )

F. AzarpanahM. Karavan — 2005

Czechoslovak Mathematical Journal

The spaces X in which every prime z -ideal of C ( X ) is either minimal or maximal are characterized. By this characterization, it turns out that for a large class of topological spaces X , such as metric spaces, basically disconnected spaces and one-point compactifications of discrete spaces, every prime z -ideal in C ( X ) is either minimal or maximal. We will also answer the following questions: When is every nonregular prime ideal in C ( X ) a z -ideal? When is every nonregular (prime) z -ideal in C ( X ) a z -ideal? For...

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