The Kirch space is topologically rigid

Taras Banakh; Yaryna Stelmakh; Sławomir Turek

doi:10.1016/j.topol.2021.107782

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arXiv · 2006.12357

The Kirch space is topologically rigid

Taras Banakh·Yaryna Stelmakh·Sławomir Turek

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Abstract

The $Golomb$ $space$ (resp. the $Kirch$ $space$) is the set $\mathbb N$ of positive integers endowed with the topology generated by the base consisting of arithmetic progressions $a+b\mathbb N_0=\{a+bn:n\ge 0\}$ where $a\in\mathbb N$ 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.

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BibTeX RIS

Taras Banakh, Yaryna Stelmakh, Sławomir Turek. 2020-07-07. The Kirch space is topologically rigid. https://doi.org/10.1016/j.topol.2021.107782

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