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

On a Homeomorphism between the Sorgenfrey Line S and Its Modification S P A topological space S P , which is a modification of the Sorgenfrey line S, is considered. It is defined as follows: if x ∈ P ⊂ S, then a base of neighborhoods of x is the family {[x, x + ε), ε > 0} of half-open intervals, and if x ∈ S P, then a base of neighborhoods of x is the family {(x − ε, 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 x ∈ P to be the same as in the natural topology of the real line. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Notes Springer Journals

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

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Publisher
Pleiades Publishing
Copyright
Copyright © 2018 by Pleiades Publishing, Ltd.
Subject
Mathematics; Mathematics, general
ISSN
0001-4346
eISSN
1573-8876
D.O.I.
10.1134/S0001434618010273
Publisher site
See Article on Publisher Site

Abstract

A topological space S P , which is a modification of the Sorgenfrey line S, is considered. It is defined as follows: if x ∈ P ⊂ S, then a base of neighborhoods of x is the family {[x, x + ε), ε > 0} of half-open intervals, and if x ∈ S P, then a base of neighborhoods of x is the family {(x − ε, 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 x ∈ P to be the same as in the natural topology of the real line.

Journal

Mathematical NotesSpringer Journals

Published: Mar 14, 2018

References

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