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On the differences of upper semicontinuous quasi-continuous functions. (English) Zbl 0941.26002
The paper deals with the characterization of the difference of upper semicontinuous quasi-continuous functions by means the extreme limits on the set of continuity points. In detail if \(f_1\) and \(f_2\) are upper semicontinuous functions such that \(f_1 - f_2\) is Darboux and quasi-continuous, then \(f_1 - f_2\) can be written as a difference of two Darboux upper semicontinuous functions.
MSC:
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
54C08 Weak and generalized continuity
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References:
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