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On determining sets for certain generalizations of continuity. (English) Zbl 0624.54009
A set \(D\subset X\) is called a determining set for a family of mappings \(F_{X,Y}\subset Y^ X\) if for any pair \(f,g\in F_{X,Y}\) the equality \(f| D=g| D\) implies \(f=g\). The author investigates determining sets for classes of quasicontinuous and somewhat continuous maps of topological spaces, and proves that for an arbitrary topological space X and a Urysohn space Y the systems of all determining sets for families of all quasicontinuous maps and families of all quasicontinuous two-valued characteristic maps coincide. He also characterizes determining sets. An analogous result is obtained for the case of somewhat continuous maps. Certain sufficient conditions under which determining families are singletons formed by the whole domain space only are also discussed.
Reviewer: J.Chvalina

MSC:
54C08 Weak and generalized continuity
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References:
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