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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2021, Volume 18, Issue 2, Pages 1735–1741
DOI: https://doi.org/10.33048/semi.2021.18.133 (Mi semr1474) 		 
Geometry and topology

Continuous bijections of Borel subsets of the Sorgenfrey line on compact spaces

V. R. Smolin

Krasovskii Institute of Mathematics and Mechanics, 16, Sofia Kovalevskaya str., Ekaterinburg, 620990, Russia
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DOI: https://doi.org/10.33048/semi.2021.18.133
Abstract: We prove that the topology of an uncountable Borel subset of the Sorgenfrey line is equal to the supremum of metrizable compact topologies. As a corollary we obtain that a Borel subset of the Sorgenfrey line has a weak Hausdorff compact topology if and only if it is either uncountable or countable and scattered.
Keywords: Sorgenfrey line, Borel set, supremum of topologies, compact condensation, weak compact topology, Lusin scheme.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2021-1383
Received October 25, 2019, published December 30, 2021
Bibliographic databases:
Document Type: Article
UDC: 515.126
MSC: 54C10
Language: Russian
Citation: V. R. Smolin, “Continuous bijections of Borel subsets of the Sorgenfrey line on compact spaces”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 1735–1741
Citation in format AMSBIB
\Bibitem{Smo21}
\by V.~R.~Smolin
\paper Continuous bijections of Borel subsets of the Sorgenfrey line on compact spaces
\jour Sib. \`Elektron. Mat. Izv.
\yr 2021
\vol 18
\issue 2
\pages 1735--1741
\mathnet{http://mi.mathnet.ru/semr1474}
\crossref{https://doi.org/10.33048/semi.2021.18.133}
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