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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.)