Geodesic
Theorems on the representability of spaces as unions of at most countably many homogeneous subspaces
Matematičeskie zametki, Tome 116 (2024) no. 2, pp. 261-265.

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A topological space $X$ is said to be homogeneous if for any $x, y\in X$ there exists a self-homeomorphism $f$ of $X$ such that $f(x)=y$. We propose a method for constructing topological spaces representable as a union of $n$ but not fewer homogeneous subspaces, where $n$ is an arbitrary given positive integer. Further, we present a solution of a similar problem for the case of infinitely many summands.
Keywords: homogeneous topological space, topological sum of spaces, small inductive dimension. 
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S. M. Komov. Theorems on the representability of spaces as unions of at most countably many homogeneous subspaces. Matematičeskie zametki, Tome 116 (2024) no. 2, pp. 261-265. http://geodesic.mathdoc.fr/item/MZM_2024_116_2_a7/

[1] R. Engelking, Obschaya topologiya, Mir, M., 1986 | MR

[2] A. V. Arhangel'skii, J. van Mil, “Topological homogeneity”, Recent Progress in General Topology. III, Atlantis Press, Paris, 2014, 1–68 | MR

[3] A. V. Arkhangelskii, “Topologicheskaya odnorodnost. Topologicheskie gruppy i ikh nepreryvnye obrazy”, UMN, 42:2 (254) (1987), 69–105 | MR | Zbl