Geodesic
On modification of the Sorgenfrey line
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 46 (2017), pp. 36-40 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we consider a topological space $S_A$ that is a modification of the Sorgenfrey line $S$ and is defined as follows: if a point $x\in A\subset \mathbf{R}$, then the base of neighborhoods of the point is $\{[x, x+\varepsilon), \forall\varepsilon>0\}$; if a point $x\in \mathbf{R}\setminus A$, then the base of neighborhoods of the point is $\{(x-\varepsilon, x], \forall\varepsilon>0\}$. The following criterion for a homeomorphism of the spaces $S_A$ and $S_Q$ has been obtained: the spaces $S_A$ and $S_Q$ are homeomorphic if and only if a subset $A\subset S_A$ is countable and dense in $S$.
Keywords: Sorgenfrey line, homeomorphism, the space of the second category.
Mots-clés : Baire space 
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E. S. Sukhacheva; T. E. Khmyleva. On modification of the Sorgenfrey line. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 46 (2017), pp. 36-40. http://geodesic.mathdoc.fr/item/VTGU_2017_46_a4/

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