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A unified theory of closed functions. (English) Zbl 1119.54304

Summary: We obtain some characterizations and several properties of \(M\)-closed functions defined between sets satisfying some minimal conditions. The functions enable us to formulate a unified theory of modifications of closedness: \(\alpha\)-closedness, semi-closedness, preclosedness and \(\beta\)-closedness.

MSC:

54A05 Topological spaces and generalizations (closure spaces, etc.)
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
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