Geodesic
On modification of the Sorgenfrey line
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 46 (2017), pp. 36-40

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

In this paper, we consider a topological space $S_A$ that is a modification of the Sorgenfrey line $S$ and is defined as follows: if a point $x\in A\subset \mathbf{R}$, then the base of neighborhoods of the point is $\{[x, x+\varepsilon), \forall\varepsilon>0\}$; if a point $x\in \mathbf{R}\setminus A$, then the base of neighborhoods of the point is $\{(x-\varepsilon, x], \forall\varepsilon>0\}$. The following criterion for a homeomorphism of the spaces $S_A$ and $S_Q$ has been obtained: the spaces $S_A$ and $S_Q$ are homeomorphic if and only if a subset $A\subset S_A$ is countable and dense in $S$.
Keywords: Sorgenfrey line, homeomorphism, the space of the second category.
Mots-clés : Baire space 
@article{VTGU_2017_46_a4,
     author = {E. S. Sukhacheva and T. E. Khmyleva},
     title = {On modification of the {Sorgenfrey} line},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {36--40},
     publisher = {mathdoc},
     number = {46},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2017_46_a4/}
}
TY  - JOUR
AU  - E. S. Sukhacheva
AU  - T. E. Khmyleva
TI  - On modification of the Sorgenfrey line
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2017
SP  - 36
EP  - 40
IS  - 46
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VTGU_2017_46_a4/
LA  - ru
ID  - VTGU_2017_46_a4
ER  - 
%0 Journal Article
%A E. S. Sukhacheva
%A T. E. Khmyleva
%T On modification of the Sorgenfrey line
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2017
%P 36-40
%N 46
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VTGU_2017_46_a4/
%G ru
%F VTGU_2017_46_a4
E. S. Sukhacheva; T. E. Khmyleva. On modification of the Sorgenfrey line. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 46 (2017), pp. 36-40. http://geodesic.mathdoc.fr/item/VTGU_2017_46_a4/