Geodesic
On sequences which are not uniformly converging on any open subset
Serdica Mathematical Journal, Tome 49 (2023) no. 1–3, pp. 107-126.

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

We consider the property of nonuniform convergence to 0 of a sequence of functions on any open subset of a metric space. We consider three examples with respect to three different characteristics. Next we show that the three characteristics cannot be present simultaneously. For this purpose we introduce the so-called height function, which we use to quantify how far is a sequence of functions from satisfying any of the third characteristic. Moreover, we study properties of the height function and its relation to uniform convergence. Finally, we show that this quantification is precise.
Keywords: sequence of functions, nonuniform convergence, 54A20, 26A15, 40A30 
@article{SMJ2_2023_49_1_3_a6,
     author = {Apostolov, Stoyan and Petrov, Zhivko},
     title = {On sequences which are not uniformly converging on any open subset},
     journal = {Serdica Mathematical Journal},
     pages = {107--126},
     publisher = {mathdoc},
     volume = {49},
     number = {1{\textendash}3},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2023_49_1_3_a6/}
}
TY  - JOUR
AU  - Apostolov, Stoyan
AU  - Petrov, Zhivko
TI  - On sequences which are not uniformly converging on any open subset
JO  - Serdica Mathematical Journal
PY  - 2023
SP  - 107
EP  - 126
VL  - 49
IS  - 1–3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SMJ2_2023_49_1_3_a6/
LA  - en
ID  - SMJ2_2023_49_1_3_a6
ER  - 
%0 Journal Article
%A Apostolov, Stoyan
%A Petrov, Zhivko
%T On sequences which are not uniformly converging on any open subset
%J Serdica Mathematical Journal
%D 2023
%P 107-126
%V 49
%N 1–3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SMJ2_2023_49_1_3_a6/
%G en
%F SMJ2_2023_49_1_3_a6
Apostolov, Stoyan; Petrov, Zhivko. On sequences which are not uniformly converging on any open subset. Serdica Mathematical Journal, Tome 49 (2023) no. 1–3, pp. 107-126. http://geodesic.mathdoc.fr/item/SMJ2_2023_49_1_3_a6/