On a weak form of uniform convergence
Commentationes Mathematicae Universitatis Carolinae (2005)
- Volume: 46, Issue: 4, page 637-643
- ISSN: 0010-2628
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topFuka, Jaroslav, and Holický, Petr. "On a weak form of uniform convergence." Commentationes Mathematicae Universitatis Carolinae 46.4 (2005): 637-643. <http://eudml.org/doc/249560>.
@article{Fuka2005,
abstract = {The notion of $\Delta $-convergence of a sequence of functions is stronger than pointwise convergence and weaker than uniform convergence. It is inspired by the investigation of ill-posed problems done by A.N. Tichonov. We answer a question posed by M. Katětov around 1970 by showing that the only analytic metric spaces $X$ for which pointwise convergence of a sequence of continuous real valued functions to a (continuous) limit function on $X$ implies $\Delta $-convergence are $\sigma $-compact spaces. We show that the assumption of analyticity cannot be omitted.},
author = {Fuka, Jaroslav, Holický, Petr},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {continuous functions on metric spaces; pointwise convergence; $\Delta $-convergence; analytic spaces; Hurewicz theorem; $K_\sigma $-spaces; continuous functions on metric spaces; pointwise convergence; -convergence; analytic space; Hurewicz theorem; -compact space},
language = {eng},
number = {4},
pages = {637-643},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On a weak form of uniform convergence},
url = {http://eudml.org/doc/249560},
volume = {46},
year = {2005},
}
TY - JOUR
AU - Fuka, Jaroslav
AU - Holický, Petr
TI - On a weak form of uniform convergence
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 4
SP - 637
EP - 643
AB - The notion of $\Delta $-convergence of a sequence of functions is stronger than pointwise convergence and weaker than uniform convergence. It is inspired by the investigation of ill-posed problems done by A.N. Tichonov. We answer a question posed by M. Katětov around 1970 by showing that the only analytic metric spaces $X$ for which pointwise convergence of a sequence of continuous real valued functions to a (continuous) limit function on $X$ implies $\Delta $-convergence are $\sigma $-compact spaces. We show that the assumption of analyticity cannot be omitted.
LA - eng
KW - continuous functions on metric spaces; pointwise convergence; $\Delta $-convergence; analytic spaces; Hurewicz theorem; $K_\sigma $-spaces; continuous functions on metric spaces; pointwise convergence; -convergence; analytic space; Hurewicz theorem; -compact space
UR - http://eudml.org/doc/249560
ER -
References
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