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On H-closed and U-closed functions. (English) Zbl 1274.54042

Summary: We extend the work on H-closed functions started by F. Cammaroto, V. V. Fedorchuk and J. Porter [Commentat. Math. Univ. Carol. 39, No. 3, 563–572 (1998; Zbl 0962.54011)]. Also, U-closed functions are introduced and characterized in terms of filters and adherence. The hereditary and productivity properties are examined and developed for both H-closed and U-closed functions.

MSC:

54B05 Subspaces in general topology
54B10 Product spaces in general topology
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54D25 “\(P\)-minimal” and “\(P\)-closed” spaces
54G20 Counterexamples in general topology

Citations:

Zbl 0962.54011
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