On modification of the Sorgenfrey line
In this paper, we consider a topological space SA that is a modification of the Sorgenfrey line S and is defined as follows: if a point x е A с R , then the base of neighborhoods of the point is {[x, x + e), Ve> 0} ; if a point x е R \ A , then the base of neighborhoods of the point is {(x -e, x], Ve > 0} . The following criterion for a homeomorphism of the spaces SA and Sq has been obtained: the spaces SA and Sq are homeomorphic if and only if a subset A с SA is countable and dense in S .
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Keywords
the space of the second category, homeomorphism, Baire space, Sorgenfrey line, пространство второй категории, бэровское пространство, Прямая Зоргенфрея, гомеоморфизмAuthors
| Name | Organization | |
| Sukhacheva Elena Sergevna | Tomsk State University | sirius9113@mail.ru |
| Khmyleva Tatiana Evgenievna | Tomsk State University | TEX2150@yandex.ru |
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On modification of the Sorgenfrey line | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2017. № 46. DOI: 10.17223/19988621/46/5
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