On the homeomorphism of the sorgenfrey line and its modifications Sq | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2016. № 1(39).

On the homeomorphism of the sorgenfrey line and its modifications Sq

In this paper, it is proved that two topological spaces, namely, the Sorgenfrey line S and its modifications Sq , where Q is the set of rational numbers on the real line, are nonhomeomorphic. Topology of the space Sq is defined as follows: if х е Q с S , then the base of neighborhoods of the point х is the family of semiintervals {[х,х + е): е > 0} ,and if х е S \ Q , then the base of the neighborhood is a family of semiintervals {(х -е, х]: е > 0}. The proof of this fact uses monotonicity of the homeomorphism ф: S ^ S on some interval (a, b) с S (E.K. Van Douwen, 1979).

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Keywords

homeomorphism, first category set, Baire space, Sorgenfrey line, множество первой категории, бэровское пространство, гомеоморфизм, стрелка Зоргенфрея

Authors

Name	Organization	E-mail
Khmyleva Tatiana Evgenievna	Tomsk State University	TEX2150@yandex.ru

Всего: 1

References

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Van Douwen E.K. Retracts of the Sorgenfrey line // Compositio Mathematica. 1979. Т. 38. No. 2. P. 155-161.

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Хмылева Т.Е., Сухачева Е.С. О некоторых линейно упорядоченных топологических пространствах, гомеоморфных прямой Зоргенфрея // Вестник Томского государственного университета. Математика и механика. 2014. № 5.