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On the connectivity for Darboux functions. (English) Zbl 0587.26001
For the class \(D^*\) of all functions \(f: R\to R\) for which \(f(I)=R\) for every nondegenerate interval I, the authors proved the following Theorem: For a subset A of R there exists such a function f of \(D^*\) that A is the set of all points of R at which f is connected in the sense of B. D. Garrett, D. Nelms and K. R. Kellum [Jahresber. Dtsch. Math.- Ver. 73, 131-137 (1971; Zbl 0226.26006)] iff A contains all its bilateral limit points.
Reviewer: L.Mišík
MSC:
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
Citations:
Zbl 0226.26006
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References:
[1] BRUCKNER A. M., CEDER J. G.: Darboux continuity. Jber. Deutsch. Math.-Verein., 67, 1965, 93-117. · Zbl 0144.30003
[2] GARRETT B. D., NELMS D., KELLUM K. R.: Characterizations of connected real functions. Jber. Deutsch. Math.-Verein., 73, 1971, 131-137. · Zbl 0226.26006
[3] ROSEN H.: Connectivity points and Darboux points of real functions. Fund. Math., 89, 1975, 265-269. · Zbl 0316.26004
[4] SNOHA L.: On connectivity points. Math. Slovaca, 33, 1983, 59-67. · Zbl 0517.26005
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