Charachterizations of pre-\(R_0\), pre-\(R_1\) spaces and \(p^*\)-closedness of strongly compact (countably \(p\)-compact) sets
We introduce \(p^*\)-closed sets and obtain new characterizations of pre-\(R_0\) and pre-\(R_1\) spaces. Necessary and sucient conditions are obtained for
the \(p^*\)-closedness of a strongly compact (countably \(p\)-compact) set in pre-\(R_1\) (pre-sequential, pre-\(R_1\)), \(p\)-normal (pre-sequential, p-normal)and also in \(p^*\)-normal (pre- sequential, \(p^*\)-normal) spaces introduced in the paper.
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