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A unified theory of weakly open functions. (English) Zbl 1181.54023

Summary: We introduce a new notion of weakly \(M\)-open functions as functions defined between sets satisfying some minimal conditions. We obtain some characterizations and several properties of such functions. The functions enable us to formulate a unified theory of weak openness, weak semi-openness, weak preopenness, and weak \(\beta\)-openness.

MSC:

54C10 Special maps on topological spaces (open, closed, perfect, etc.)
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