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Maximums of Darboux quasi-continuous functions. (English) Zbl 0961.26003
Author considers two conditions, necessary and sufficient for a function \(f:\mathbb R\to \mathbb R\) to be the maximum of two Darboux quasi-continuous functions. He proves in particular that the necessary condition is not sufficient and the sufficient one is not necessary. The problem of the characterization of the maxima of Darboux quasi-continuous functions remains still open.

MSC:
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
26A21 Classification of real functions; Baire classification of sets and functions
54C08 Weak and generalized continuity
54C30 Real-valued functions in general topology
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References:
[1] BRUCKNER A. M.-CEDER J. G.: Darboux continuity. Jahresber. Deutsch. Math.-Verein. 67 (1965), 93-117. · Zbl 0144.30003
[2] KEMPISTY S.: Sur les fonctions quasicontinues. Fund. Math. 19 (1932), 184 197. · Zbl 0005.19802
[3] NATKANIEC T.: On quasi-continuous functions having Darboux property. Math. Pannon. 3 (1992), 81-96. · Zbl 0767.26005
[4] NATKANIEC T.: On the maximum and the minimum of quasi-continuous functions. Math. Slovaca 42 (1992), 103-110. · Zbl 0789.54021
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