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Mathematical Notes

, Volume 103, Issue 1–2, pp 259–270 | Cite as

On a Homeomorphism between the Sorgenfrey Line S and Its Modification S P

  • E. S. Sukhacheva
  • T. E. Khmyleva
Article

Abstract

A topological space S P , which is a modification of the Sorgenfrey line S, is considered. It is defined as follows: if xPS, then a base of neighborhoods of x is the family {[x, x + ε), ε > 0} of half-open intervals, and if xSP, then a base of neighborhoods of x is the family {(xε, x], ε > 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 xP 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 Fσ-set Gδ-set. 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.National Research Tomsk State UniversityTomskRussia
  2. 2.Université de RouenRouenFrance

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