On homeomorphisms of spaces $I\times[1,\alpha]$ with the Sorgenfrey topology
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 5 (2013), pp. 40-44
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In this paper, a topological classification of spaces $I\times[1,\alpha]$ is presented. Here, $\alpha$ is an arbitrary ordinal and the semi-interval $I=(0,1]$ is equipped with the Sorgenfrey topology. It is proved that the space $I\times[1,\alpha]$ is homeomorphic to the space $I\times[1,\beta]$ if and only if $\alpha\le\beta\alpha\cdot\omega$.
Keywords:
line of Sorgenfrey, continuous functions, linear homeomorphisms, interval of ordinals.
@article{VTGU_2013_5_a4,
author = {N. N. Trofimenko and T. E. Khmyleva},
title = {On homeomorphisms of spaces $I\times[1,\alpha]$ with the {Sorgenfrey} topology},
journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
pages = {40--44},
publisher = {mathdoc},
number = {5},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VTGU_2013_5_a4/}
}
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N. N. Trofimenko; T. E. Khmyleva. On homeomorphisms of spaces $I\times[1,\alpha]$ with the Sorgenfrey topology. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 5 (2013), pp. 40-44. http://geodesic.mathdoc.fr/item/VTGU_2013_5_a4/