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 $a,b\in \mathbb{N}$ 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.

中文翻译：

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Kirch 空间是拓扑刚性的

的哥伦布空间（分别在基尔希空间）是该组$\mathbb{N}$ 具有由等差数列组成的基生成的拓扑的正整数 $\mathrm{一种}+乙{\mathbb{N}}_0=\{\mathrm{一种}+乙n：n\ge 0\}$ 在哪里 $\mathrm{一种},乙\in \mathbb{N}$和b是（ -自由正方形）号码，互质与一个。众所周知，Golomb 空间（分别是 Kirch 空间）是连通的（并且是局部连通的）。根据 Banakh、Spirido 和 Turek 的最新结果，Golomb 空间具有平凡同胚群，因此是拓扑刚性的。在本文中，我们证明了 Kirch 空间的拓扑刚性。