The Kirch space is topologically rigid

The Golomb space (resp. the Kirch space) is the set N of positive integers endowed with the topology generated by the base consisting of arithmetic progressions a+bN0={a+bn:n≥0} where a,b∈N and b is a (square-free) number, coprime with a. It is known that the Golomb space (resp. the Kirch space) is...

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Bibliographic Details
Published in:Topology and its applications 2021-12, Vol.304, p.107782, Article 107782
Main Authors: Banakh, Taras, Stelmakh, Yaryna, Turek, Sławomir
Format: Article
Language:English
Subjects:
Arithmetic progression
The Kirch topology
Topologically rigid space
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Summary:The Golomb space (resp. the Kirch space) is the set N of positive integers endowed with the topology generated by the base consisting of arithmetic progressions a+bN0={a+bn:n≥0} where a,b∈N and b is a (square-free) number, coprime with a. It is known that the Golomb space (resp. the Kirch space) is connected (and locally connected). By a recent result of Banakh, Spirito and Turek, the Golomb space has trivial homeomorphism group and hence is topologically rigid. In this paper we prove the topological rigidity of the Kirch space.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2021.107782