Geodesic
On a weak form of uniform convergence
Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 4, pp. 637-643.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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. Kat\v{e}tov 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.
Classification : 40A30, 54E35, 54H05
Keywords: continuous functions on metric spaces; pointwise convergence; $\Delta $-convergence; analytic spaces; Hurewicz theorem; $K_\sigma $-spaces 
@article{CMUC_2005__46_4_a3,
     author = {Fuka, Jaroslav and Holick\'y, Petr},
     title = {On a weak form of uniform convergence},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {637--643},
     publisher = {mathdoc},
     volume = {46},
     number = {4},
     year = {2005},
     mrnumber = {2259495},
     zbl = {1121.54058},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2005__46_4_a3/}
}
TY  - JOUR
AU  - Fuka, Jaroslav
AU  - Holický, Petr
TI  - On a weak form of uniform convergence
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2005
SP  - 637
EP  - 643
VL  - 46
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2005__46_4_a3/
LA  - en
ID  - CMUC_2005__46_4_a3
ER  - 
%0 Journal Article
%A Fuka, Jaroslav
%A Holický, Petr
%T On a weak form of uniform convergence
%J Commentationes Mathematicae Universitatis Carolinae
%D 2005
%P 637-643
%V 46
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2005__46_4_a3/
%G en
%F CMUC_2005__46_4_a3
Fuka, Jaroslav; Holický, Petr. On a weak form of uniform convergence. Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 4, pp. 637-643. http://geodesic.mathdoc.fr/item/CMUC_2005__46_4_a3/