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