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The discontinuity point set of A-continuous functions (in Ukrainian)

Keywords: A-continuous function , discontinuity point set , quasi-continuous function , linearly continuous function , A-nowhere dense set , σ -A-nowhere dense set

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Abstract:

We characterize the set of discontinuity points of A-continuous quasi-continuous functions of the first class defined on hereditarily normal weakly pairwise attainable spaces. Besides, we obtain several sufficient properties of a subset of a normed space which guarantee an existence of a linearly continuous function with the given discontinuity point set.

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