Geodesic
Defining a~metric in a~linear space by means of a~family of subsets
Matematičeskie zametki, Tome 19 (1976) no. 2, pp. 237-246.

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

Necessary and sufficient conditions are given on a family $\{A_r\}_{r>0}$ of subsets of a real linear space $X$ under which $\inf\{r>0:x\in A_r\}$ is a quasinorm [1] on X. It is shown that for any symmetric (about zero) closed set $A$ in a normed space $X$ containing the ball $\{x\in X:\|x\|\le1\}$ there exists a quasinorm $|\cdot|$ on $X$ such that $A=\{x\in X:\|x\|\le1\}$. Examples are constructed of linear metric spaces in which there exists a Chebyshev line which is not an approximately compact set. 
@article{MZM_1976_19_2_a8,
     author = {A. I. Vasil'ev},
     title = {Defining a~metric in a~linear space by means of a~family of subsets},
     journal = {Matemati\v{c}eskie zametki},
     pages = {237--246},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_2_a8/}
}
TY  - JOUR
AU  - A. I. Vasil'ev
TI  - Defining a~metric in a~linear space by means of a~family of subsets
JO  - Matematičeskie zametki
PY  - 1976
SP  - 237
EP  - 246
VL  - 19
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1976_19_2_a8/
LA  - ru
ID  - MZM_1976_19_2_a8
ER  - 
%0 Journal Article
%A A. I. Vasil'ev
%T Defining a~metric in a~linear space by means of a~family of subsets
%J Matematičeskie zametki
%D 1976
%P 237-246
%V 19
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1976_19_2_a8/
%G ru
%F MZM_1976_19_2_a8
A. I. Vasil'ev. Defining a~metric in a~linear space by means of a~family of subsets. Matematičeskie zametki, Tome 19 (1976) no. 2, pp. 237-246. http://geodesic.mathdoc.fr/item/MZM_1976_19_2_a8/