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Generalized locally closed sets and \(GLC\)-continuous functions. (English) Zbl 0851.54002

A subset \(S\) of a topological space \(X\) is called locally closed if \(S\) is the intersection of an open set and a closed set. This notion was investigated in a paper by I. Reilly and the reviewer [Int. J. Math. Math. Sci. 12, 417-424 (1989; Zbl 0676.54014)] in which they also introduced and studied the related notions of LC-irresoluteness, LC-continuity and sub-LC-continuity of functions.
In the present paper the authors replace ‘locally closed’ by ‘generalized locally closed’, where a subset is generalized locally closed if it is the intersection of a g-open and a g-closed set, and they prove a bunch of results in the spirit of the above mentioned paper by Reilly and the reviewer.
Reviewer: M.Ganster (Graz)

MSC:

54A05 Topological spaces and generalizations (closure spaces, etc.)
54C08 Weak and generalized continuity

Citations:

Zbl 0676.54014
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