Geodesic
Classification of semispaces according to their types in infinite-dimensional vector spaces
Matematičeskie zametki, Tome 64 (1998) no. 2, pp. 191-198

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

It is shown that each semispace $C\subset X$ naturally generates a relation of complete preorder on $X$ with respect to which the pair $(setminus C,C)$ is a cut of $X$. By identifying the type of the semispace with the type of the cut generated by this semispace, the semispaces are classified according to their types. The obtained classification extends the classification of semispaces in finite-dimensional vector spaces due to Martinez-Legaz and Singer to infinite-dimensional spaces. 
@article{MZM_1998_64_2_a3,
     author = {V. V. Gorokhovik and E. A. Semenkova},
     title = {Classification of semispaces according to their types in infinite-dimensional vector spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {191--198},
     publisher = {mathdoc},
     volume = {64},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a3/}
}
TY  - JOUR
AU  - V. V. Gorokhovik
AU  - E. A. Semenkova
TI  - Classification of semispaces according to their types in infinite-dimensional vector spaces
JO  - Matematičeskie zametki
PY  - 1998
SP  - 191
EP  - 198
VL  - 64
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a3/
LA  - ru
ID  - MZM_1998_64_2_a3
ER  - 
%0 Journal Article
%A V. V. Gorokhovik
%A E. A. Semenkova
%T Classification of semispaces according to their types in infinite-dimensional vector spaces
%J Matematičeskie zametki
%D 1998
%P 191-198
%V 64
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a3/
%G ru
%F MZM_1998_64_2_a3
V. V. Gorokhovik; E. A. Semenkova. Classification of semispaces according to their types in infinite-dimensional vector spaces. Matematičeskie zametki, Tome 64 (1998) no. 2, pp. 191-198. http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a3/