Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

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

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]