Geodesic
Density of the Points of Continuity of the Metric Function and Projection in Asymmetric Spaces
Matematičeskie zametki, Tome 112 (2022) no. 6, pp. 924-934

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

Questions concerning the density of the sets of points of continuity of metric functions and metric projection onto sets in asymmetric spaces are studied.
Keywords: asymmetric space, convex set, metric function, metric projection. 
I. G. Tsar'kov. Density of the Points of Continuity of the Metric Function and Projection in Asymmetric Spaces. Matematičeskie zametki, Tome 112 (2022) no. 6, pp. 924-934. http://geodesic.mathdoc.fr/item/MZM_2022_112_6_a10/
@article{MZM_2022_112_6_a10,
     author = {I. G. Tsar'kov},
     title = {Density of the {Points} of {Continuity} of the {Metric} {Function} and {Projection} in {Asymmetric} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {924--934},
     year = {2022},
     volume = {112},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_6_a10/}
}
TY  - JOUR
AU  - I. G. Tsar'kov
TI  - Density of the Points of Continuity of the Metric Function and Projection in Asymmetric Spaces
JO  - Matematičeskie zametki
PY  - 2022
SP  - 924
EP  - 934
VL  - 112
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MZM_2022_112_6_a10/
LA  - ru
ID  - MZM_2022_112_6_a10
ER  - 
%0 Journal Article
%A I. G. Tsar'kov
%T Density of the Points of Continuity of the Metric Function and Projection in Asymmetric Spaces
%J Matematičeskie zametki
%D 2022
%P 924-934
%V 112
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_2022_112_6_a10/
%G ru
%F MZM_2022_112_6_a10

[1] S. Cobzas, “Separation of convex sets and best approximation in spaces with asymmetric norm”, Quaest. Math., 27:3 (2004), 275–296 | DOI | MR | Zbl

[2] Ş. Cobzaş, Functional Analysis in Asymmetric Normed Spaces, Front. Math., Birkhäuser, Basel, 2013 | DOI | MR | Zbl

[3] V. Donju$\acute{a}$n, N. Jonard-P$\acute{e}$rez, “Separation axioms and covering dimension of asymmetric normed spaces”, Quaest. Math., 43:4 (2020), 467–491 | DOI | MR | Zbl

[4] A. R. Alimov, “Teorema Banakha–Mazura dlya prostranstv s nesimmetrichnym rasstoyaniem”, UMN, 58:2 (350) (2003), 159–160 | DOI | MR | Zbl

[5] A. R. Alimov, “O strukture dopolneniya k chebyshevskim mnozhestvam”, Funkts. analiz i ego prilozh., 35:3 (2001), 19–27 | DOI | MR | Zbl

[6] A. R. Alimov, “Vypuklost ogranichennykh chebyshevskikh mnozhestv v konechnomernykh prostranstvakh s nesimmetrichnoi normoi”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:4 (2) (2014), 489–497 | DOI | Zbl

[7] I. G. Tsarkov, “Approksimativnye svoistva mnozhestv i nepreryvnye vyborki”, Matem. sb., 211:8 (2020), 132–157 | DOI | MR | Zbl

[8] I. G. Tsarkov, “Slabo monotonnye mnozhestva i nepreryvnaya vyborka v nesimmetrichnykh prostranstvakh”, Matem. sb., 210:9 (2019), 129–152 | DOI | MR | Zbl

[9] I. G. Tsarkov, “Nepreryvnye vyborki iz operatorov metricheskoi proektsii i ikh obobschenii”, Izv. RAN. Ser. matem., 82:4 (2018), 199–224 | DOI | MR | Zbl

[10] I. G. Tsarkov, “Nepreryvnye vyborki v nesimmetrichnykh prostranstvakh”, Matem. sb., 209:4 (2018), 95–116 | DOI | MR | Zbl

[11] I. G. Tsarkov, “Svoistva monotonno lineino svyaznykh mnozhestv”, Izv. RAN. Ser. matem., 85:2 (2021), 142–171 | DOI | MR | Zbl

[12] I. G. Tsarkov, “Uniformly and locally convex asymmetric spaces”, Russ. J. Math. Phys., 29:1 (2022), 141–148 | DOI | MR | Zbl

[13] A. R. Alimov, I. G. Tsar'kov, “Ball-complete sets and solar properties of sets in asymmetric spaces”, Results Math., 77:2 (2022), 86 | DOI | MR | Zbl

[14] A. R. Alimov, I. G. Tsar'kov, “Suns, moons, and $\mathring B$-complete sets in asymmetric spaces”, Set-Valued Var. Anal., 30:3 (2022), 1233–1245 | MR | Zbl

[15] A. R. Alimov, I. G. Tsarkov, “$B$-polnye mnozhestva i ikh approksimativnye i strukturnye svoistva”, Sib. matem. zhurn., 63:3 (2022), 500–509 | DOI | Zbl

[16] I. G. Tsarkov, “Ravnomernaya vypuklost v nesimmetrichnykh prostranstvakh”, Matem. zametki, 110:5 (2021), 773–785 | DOI | Zbl

[17] M. D. Mabula, S. Cobzas, “Zabrejko's lemma and the fundamental principles of functional analysis in the asymmetric case”, Topology Appl., 184 (2015), 1–15 | DOI | MR | Zbl

[18] M. Bachir, “Asymmetric normed Baire space”, Results Math., 76:4 (2021), 1–9 | DOI | MR

[19] M. Bachirc, G. Flores, “Index of symmetry and topological classification of asymmetric normed spaces”, Rocky Mountain J. Math., 50:6 (2020), 1951–1964 | MR