Geodesic
Metric Space of All $N$-nets of a Geodesic Space
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 136-149
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In this paper we endow the sets of all $N$-nets and of all $N$-nets with repetitions of a geodesic space with metrics. We find the conditions under which these spaces are spaces with intrinsic metrics, proper and geodesic spaces.
Mots-clés : $N$-net, segment
Keywords: geodesic space, intrinsic metric, Hausdorff metric, proper space. 
@article{UZKU_2009_151_4_a10,
     author = {E. N. Sosov},
     title = {Metric {Space} of {All} $N$-nets of {a~Geodesic} {Space}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {136--149},
     year = {2009},
     volume = {151},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a10/}
}
TY  - JOUR
AU  - E. N. Sosov
TI  - Metric Space of All $N$-nets of a Geodesic Space
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2009
SP  - 136
EP  - 149
VL  - 151
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a10/
LA  - ru
ID  - UZKU_2009_151_4_a10
ER  - 
%0 Journal Article
%A E. N. Sosov
%T Metric Space of All $N$-nets of a Geodesic Space
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2009
%P 136-149
%V 151
%N 4
%U http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a10/
%G ru
%F UZKU_2009_151_4_a10
E. N. Sosov. Metric Space of All $N$-nets of a Geodesic Space. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 136-149. http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a10/

[1] Fedorchuk V. V., Filippov V. V., “Topologiya giperprostranstv i ee prilozheniya”, Matem. kibernetika, 1989, no. 4, 1–48 | MR

[2] Kuratovskii K., Topologiya, T. 1, Mir, M., 1966, 594 pp. | MR

[3] Burago Yu. D., Gromov M. L., Perelman G. D., “Prostranstva A. D. Aleksandrova s ogranichennymi snizu kriviznami”, Usp. matem. nauk, 47:2 (1992), 3–51 | MR | Zbl

[4] Buzeman G., Geometriya geodezicheskikh, Fizmatgiz, M., 1962, 503 pp. | MR

[5] Bridson M. R., Haeffliger A. A., “Metric spaces of non-positive curvature”, Grundlehren Math. Wiss., 319, Springer-Verlag, Berlin, 1999, 643 pp. | DOI | MR | Zbl

[6] Bing R. H., “A convex metric with unique segments”, Proc. AMS, 4 (1953), 167–174 | DOI | MR | Zbl

[7] Garkavi A. L., “O nailuchshei seti i nailuchshem sechenii mnozhestv v normirovannom prostranstve”, Izv. AN SSSR. Ser. matem., 26:1 (1962), 87–106 | MR | Zbl

[8] Burago D. Yu., Burago Yu. D., Ivanov S. V., Kurs metricheskoi geometrii, In-t kompyut. issled., Moskva–Izhevsk, 2004, 496 pp.

[9] Foertsch T., Isometries of spaces of convex compact subsets of $CAT(0)$-spaces, , 21 Apr. 2004 arxiv: math/0404380v1[math.MG]

[10] Sosov E. N., “On Hausdorff intrinsic metric”, Lobachevskii J. Math., 8 (2001), 185–189 | MR | Zbl