Geodesic
On upper topological limit of family of vector subspaces of codimension~$k$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 432-435.

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

Let $\{L_\alpha\mid \alpha\in I\}$ be an infinite family of subspaces in a topological vector space $X$ the codimension of each of which is at most $k$. We prove that there exists a subspace $L\subset X$, $\operatorname{codim} L\leq k$, such that every $x\in L$ is a limit point of some family $\{l_\alpha\in L_\alpha\}$.
Keywords: upper topological limit. 
@article{SEMR_2015_12_a84,
     author = {K. V. Storozhuk},
     title = {On upper topological limit of family of vector subspaces of codimension~$k$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {432--435},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a84/}
}
TY  - JOUR
AU  - K. V. Storozhuk
TI  - On upper topological limit of family of vector subspaces of codimension~$k$
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2015
SP  - 432
EP  - 435
VL  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2015_12_a84/
LA  - ru
ID  - SEMR_2015_12_a84
ER  - 
%0 Journal Article
%A K. V. Storozhuk
%T On upper topological limit of family of vector subspaces of codimension~$k$
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2015
%P 432-435
%V 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2015_12_a84/
%G ru
%F SEMR_2015_12_a84
K. V. Storozhuk. On upper topological limit of family of vector subspaces of codimension~$k$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 432-435. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a84/

[1] F. Hausdorff, Set theory, Chelsea Publishing Company, New York, 1957 | MR | Zbl

[2] K. Kuratowski, Topology, v. I, 1966 | MR

[3] O. V. Vasil'ev, Metody optimizatsii, v. 1, 2011

[4] A. V. Arutyunov, N. T. Tynyanskii, “On necessary conditions for a local minimum in optimal control theory”, Dokl. Akad. Nauk SSSR, 275:2 (1984), 268–272 (Russian) | MR | Zbl

[5] A. V. Arutyunov, “On necessary conditions for optimality in a problem with phase constraints”, Dokl. Akad. Nauk SSSR, 280:5 (1985), 1033–1037 (Russian) | MR | Zbl

[6] Izv. Math., 60:1 (1996), 39–65 | MR | Zbl

[7] Russian Math. Surveys, 67:3 (2012), 403–457 | MR | Zbl

[8] W. W. Comfort, S. Negrepontis, The theory of ultrafilters, Springer, 1974 | MR | Zbl