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On sets determined by sequences of quasi-continuous functions. (English) Zbl 1002.26004
Let X be a topological space. f:X is said to be quasi-continuous iff for pX and open sets UX, W such that pU, f(p)W, there is an open set G such that GU, f(G)W. The main problem of the paper is to find conditions, for given sets L 0 , L + , L - , assuring that there exists a sequence of quasi-continuous functions f n that is convergent on L 0 , f n + on L + and f n - on L - .
MSC:
26A15Continuity and related questions (one real variable)
26A21Classification of functions of one real variable; Baire classification
54C30Real-valued functions on topological spaces
54C08Weak and generalized continuity