On homeomorphisms of spaces х[1,а] with the Sorgenfrey topology | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2013. № 5(25).

HomeIssuesOn homeomorphisms of spaces х[1,а] with the Sorgenfrey topology | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2013. № 5(25).

On homeomorphisms of spaces х[1,а] with the Sorgenfrey topology

In this paper, a topological classification of spaces I х [1,а] is presented. Here, а is an arbitrary ordinal and the semi-interval I = (0,1] is equipped with the Sorgenfrey topology. It is proved that the space I х [1,а] is homeomorphic to the space I х [1,P] if and only if а<р< а - ю .

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Keywords

interval of ordinals, linear homeomorphisms, continuous functions, line of Sorgenfrey, отрезок ординалов, линейные гомеоморфизмы, непрерывные функции, прямая Зоргенфрея

Authors

NameOrganizationE-mail
Trofimenko Nadezhda NikolaevnaTomsk State UniversityTrofimenko@sibmail.com
Khmyleva Tatiana EvgenievnaTomsk State UniversityTEX2150@yandex.ru
Всего: 2

References

Куратовский К.,Мостовский А. Теория множеств. М.: Мир, 1970. 416 с.
Burke D.K., Moore J.T. Subspaces of the Sorgenfrey line // Topology and Its Applications. 1988. V. 90. P. 57-68.
On homeomorphisms of spaces х[1,а] with the Sorgenfrey topology | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2013. № 5(25).

On homeomorphisms of spaces х[1,а] with the Sorgenfrey topology | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2013. № 5(25).

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