The Kirch space is topologically rigid
| Autor: | Taras Banakh, Sławomir Turek, Yaryna Stelmakh |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Coprime integers
Mathematics - Number Theory 54D05 54H99 11A41 11N13 General Topology (math.GN) Homeomorphism group Space (mathematics) Base (topology) Combinatorics Computer Science::Discrete Mathematics Golomb coding FOS: Mathematics Geometry and Topology Number Theory (math.NT) Mathematics Mathematics - General Topology |
| Popis: | 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. 12 pages |
| Databáze: | OpenAIRE |
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