Geodesic
Properties of at most countable unions of~pairwise disjoint sets in asymmetric spaces
Sbornik. Mathematics, Tome 216 (2025) no. 2, pp. 257-269

Voir la notice de l'article provenant de la source Math-Net.Ru

We show that an at most countable nonsingleton union of pairwise disjoint proximinal sets is not a Chebyshev set. We also characterize the asymmetric linear spaces where each boundedly compact (approximatively compact) set is proximinal. Bibliography: 32 titles.
Keywords: asymmetric normed space, Chebyshev set, $P$-connected set, approximatively compact set, proximinal set. 
@article{SM_2025_216_2_a4,
     author = {I. G. Tsar'kov},
     title = {Properties of at most countable unions of~pairwise disjoint sets in asymmetric spaces},
     journal = {Sbornik. Mathematics},
     pages = {257--269},
     publisher = {mathdoc},
     volume = {216},
     number = {2},
     year = {2025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2025_216_2_a4/}
}
TY  - JOUR
AU  - I. G. Tsar'kov
TI  - Properties of at most countable unions of~pairwise disjoint sets in asymmetric spaces
JO  - Sbornik. Mathematics
PY  - 2025
SP  - 257
EP  - 269
VL  - 216
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2025_216_2_a4/
LA  - en
ID  - SM_2025_216_2_a4
ER  - 
%0 Journal Article
%A I. G. Tsar'kov
%T Properties of at most countable unions of~pairwise disjoint sets in asymmetric spaces
%J Sbornik. Mathematics
%D 2025
%P 257-269
%V 216
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2025_216_2_a4/
%G en
%F SM_2025_216_2_a4
I. G. Tsar'kov. Properties of at most countable unions of~pairwise disjoint sets in asymmetric spaces. Sbornik. Mathematics, Tome 216 (2025) no. 2, pp. 257-269. http://geodesic.mathdoc.fr/item/SM_2025_216_2_a4/