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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2018, Volume 103, Issue 2, Pages 258–272 (Mi mz11871)

On a Homeomorphism between the Sorgenfrey Line $S$ and Its Modification $S_P$

E. S. Sukhachevaab, T. E. Khmylevaa

a Tomsk State University
b Université de Rouen

Abstract: A topological space $S_P$, which is a modification of the Sorgenfrey line $S$, is considered. It is defined as follows: if $x\in P\subset S$, then a base of neighborhoods of $x$ is the family $\{[x,x+\varepsilon), \varepsilon>0\}$ of half-open intervals, and if $x\in S\setminus P$, then a base of neighborhoods of $x$ is the family $\{(x-\varepsilon,x], \varepsilon>0\}$. A necessary and sufficient condition under which the space $S_P$ is homeomorphic to $S$ is obtained. Similar questions were considered by V. A. Chatyrko and I. Hattori, who defined the neighborhoods of $x \in P$ to be the same as in the natural topology of the real line.

Keywords: Sorgenfrey line, point of condensation, Baire space, nowhere dense set, homeomorphism, ordinal, spaces of the first and second category, $F_\sigma$-set, $G_\delta$-set.

DOI: https://doi.org/10.4213/mzm11871

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English version:
Mathematical Notes, 2018, 103:2, 259–270

Bibliographic databases:

UDC: 515.12
Revised: 20.04.2017

Citation: E. S. Sukhacheva, T. E. Khmyleva, “On a Homeomorphism between the Sorgenfrey Line $S$ and Its Modification $S_P$”, Mat. Zametki, 103:2 (2018), 258–272; Math. Notes, 103:2 (2018), 259–270

Citation in format AMSBIB
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