Geodesic
Solarity and connectedness of sets in the space $C[a,b]$ and in finite-dimensional polyhedral spaces
Sbornik. Mathematics, Tome 213 (2022) no. 2, pp. 268-282

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

Generalized $n$-piecewise functions constructed from given monotone path-connected boundedly compact subsets of the space $C[a,b]$ are studied. They are shown to be monotone path-connected suns. In finite-dimensional polyhedral spaces, luminosity points of sets admitting a lower semicontinuous selection of the metric projection operator are investigated. An example of a non-$B$-connected sun in a four-dimensional polyhedral normed space is constructed. Bibliography: 14 titles.
Keywords: monotone path-connected set, Menger-connectedness, stably monotone path-connectedness, sun. 
@article{SM_2022_213_2_a5,
     author = {I. G. Tsar'kov},
     title = {Solarity and connectedness of sets in the space $C[a,b]$ and in finite-dimensional polyhedral spaces},
     journal = {Sbornik. Mathematics},
     pages = {268--282},
     publisher = {mathdoc},
     volume = {213},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2022_213_2_a5/}
}
TY  - JOUR
AU  - I. G. Tsar'kov
TI  - Solarity and connectedness of sets in the space $C[a,b]$ and in finite-dimensional polyhedral spaces
JO  - Sbornik. Mathematics
PY  - 2022
SP  - 268
EP  - 282
VL  - 213
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2022_213_2_a5/
LA  - en
ID  - SM_2022_213_2_a5
ER  - 
%0 Journal Article
%A I. G. Tsar'kov
%T Solarity and connectedness of sets in the space $C[a,b]$ and in finite-dimensional polyhedral spaces
%J Sbornik. Mathematics
%D 2022
%P 268-282
%V 213
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2022_213_2_a5/
%G en
%F SM_2022_213_2_a5
I. G. Tsar'kov. Solarity and connectedness of sets in the space $C[a,b]$ and in finite-dimensional polyhedral spaces. Sbornik. Mathematics, Tome 213 (2022) no. 2, pp. 268-282. http://geodesic.mathdoc.fr/item/SM_2022_213_2_a5/