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Almost \(\tilde {g}_{\alpha }\)-closed functions and separation axioms. (English) Zbl 1265.54087

Summary: We introduce a new class of functions called almost \(\tilde {g}_{\alpha }\)-closed and use the functions to improve several preservation theorems of normality and regularity and also their generalizations. The main result of the paper is that normality and weak normality are preserved under almost \(\tilde {g}_{\alpha }\)-closed continuous surjections.

MSC:

54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54C08 Weak and generalized continuity
54C05 Continuous maps
54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
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