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Zbl 1070.26005
Wesołowska, Jolanta
On sets of discrete convergence points of sequences of real functions.
(English)
[J] Real Anal. Exch. 29, No. 1, 107-120 (2003-2004). ISSN 0147-1937

For a sequence $(a_n)$ of real numbers, $a\in\bbfR$ is said to be the discrete limit of $(a_n)$ iff there exists $k\in\bbfN$ such that $a_n= a$ for $k< n$ [cf. {\it Á. Császár} and {\it M. Laczkovic}, Studia Sci. Math. Hung. 10, 463--472 (1975; Zbl 0405.26006)]. The purpose of the paper is to characterize, for different families ${\Cal F}$ of functions $f: \bbfR\to\bbfR$, the set $L^d({\Cal F})$ of points $x\in\bbfR$, where given a sequence $(f_n)\subset{\Cal F}$, $f_n(x)$ discretely converges to some limit $f(x)$. As ${\Cal F}$, Baire class $\alpha$, Darboux functions, measurable functions, derivatives, approximately continuous functions, quasi-continuous functions, etc. are considered.
[Ákos Császár (Budapest)]
MSC 2000:
*26A21 Classification of functions of one real variable
26A03 Elementary topology of the real line
54C50 Special sets of topological spaces defined by functions

Keywords: sequence of functions; sets of convergence points; discrete convergence

Citations: Zbl 0405.26006

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