zbMATH — the first resource for mathematics

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.
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
54C08 Weak and generalized continuity
Full Text: EuDML
[1] CEDER J. G.-PEARSON T. L.: A survey of Darboux Baire 1 functions. Real Anal. Exchange 9 (1983-84), 179-194. · Zbl 0579.26002
[2] CROFT H. T.: A note on Darboux continuous functions. J. London Math. Soc. 38 (1963), 9-10. · Zbl 0111.05801
[3] EWERT J.-LIPSKI T.: Lower and upper quasi-continuous functions. Demonstratio Math. 16 (1983), 85-91. · Zbl 0526.54005
[4] GRANDE Z.: Sur la quasi-continuité et la quasi-continuité approximative. Fund. Math. 129 (1988), 167-172. · Zbl 0657.26003
[5] LUKEŠ J.-MALÝ J.-ZAJÍČEK L.: Fine Topology Methods in Real Analysis and Potential Theory. Lecture Notes in Math. 1189, Springer Verlag, New York, 1986. · Zbl 0607.31001
[6] MALISZEWSKI A.: On the sums of Darboux upper semicontinuous quasi-continuous functions. Real Anal. Exchange 20 (1994-95), 244-249. · Zbl 0822.26004
[7] MALISZEWSKI A.: On the differences of Darboux upper semicontinuous functions. Real Anal. Exchange 21 (1995-96), 258-263. · Zbl 0853.26004
[8] SIERPIŇSKI W.: Sur les fonctions développables en séries absolument convergentes de fonctions continues. Fund. Math. 2 (1921), 15-27. · JFM 48.0276.01
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.