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On strongly pre-open sets and a decomposition of continuity. (English) Zbl 1120.54308

The author introduces the notion of a strongly preopen set, an openness counterpart to a \(\delta\)-set introduced by the author and C. Bandyopadhay [Bull. Calcutta Math. Soc. 83, 281–290 (1991; Zbl 0764.54001)] i.e., a condensed set defined by Y. Isomichi [Pac. J. Math. 38, 657–668 (1971; Zbl 0227.54001)]. Hence the following decomposition of continuity: A function is continuous if and only if it is \(\delta\)-continuous and S-precontinuous.

MSC:

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