Geodesic
Continuous maps between finite powers of Sorgenfrey line
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2011), pp. 85-94 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The Sorgenfrey line is the real line with topology whose base consists of all left half-open intervals. It is shown that for integers $m>1$ there is no continuous closed map of $m$th power of the Sorgenfrey line onto Sorgenfrey line, and that for integers $n>2$ there is no continuous quotient map of the square of the Sorgenfrey line onto the $n$th power of the Sorgenfrey line.
Keywords: Sorgenfrey line, finite powers of Sorgenfrey line, continuous map, closed map
Mots-clés : quotient map. 
@article{VUU_2011_3_a7,
     author = {M. A. Patrakeev},
     title = {Continuous maps between finite powers of {Sorgenfrey} line},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {85--94},
     year = {2011},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2011_3_a7/}
}
TY  - JOUR
AU  - M. A. Patrakeev
TI  - Continuous maps between finite powers of Sorgenfrey line
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2011
SP  - 85
EP  - 94
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VUU_2011_3_a7/
LA  - ru
ID  - VUU_2011_3_a7
ER  - 
%0 Journal Article
%A M. A. Patrakeev
%T Continuous maps between finite powers of Sorgenfrey line
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2011
%P 85-94
%N 3
%U http://geodesic.mathdoc.fr/item/VUU_2011_3_a7/
%G ru
%F VUU_2011_3_a7
M. A. Patrakeev. Continuous maps between finite powers of Sorgenfrey line. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2011), pp. 85-94. http://geodesic.mathdoc.fr/item/VUU_2011_3_a7/

[1] Engelking R., Obschaya topologiya, Mir, M., 1986, 751 pp. | MR

[2] Burke D. K., Lutzer D. J., “On powers of certain lines”, Topology and its applications, 26 (1987), 251–261 | DOI | MR | Zbl

[3] Patrakeev M. A., “Continuous bijections of finite powers of the Sorgenfrey line”, Proc. Steklov Inst. Math., 2004, S18–S25 | MR | Zbl

[4] Burke D. K., Moore J. T., “Subspaces of the Sorgenfrey line”, Topology and its applications, 90 (1998), 57–68 | DOI | MR | Zbl

[5] Arkhangelskii A. V., Ponomarev V. I., Osnovy obschei topologii v zadachakh i uprazhneniyakh, Nauka, M., 1974, 423 pp. | MR