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Notes on almost open mappings. (English) Zbl 1199.54076

A mapping \(f\) from a space \(X\) into a space \(Y\) is said to be almost open if for each \(y\in Y\) there is \(x\in f^{-1}(y)\) such that for each neighborhood \(U\) of \(x\), \(f(U)\) is a neighborhood of \(y\). Several properties and characterizations of almost open mappings and their relatives defined on metric and first countable spaces are given.

MSC:

54C05 Continuous maps
54C08 Weak and generalized continuity
54C10 Special maps on topological spaces (open, closed, perfect, etc.)