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. 
@article{MZM_2024_116_2_a7,
     author = {S. M. Komov},
     title = {Theorems on the representability of spaces as unions of at most countably many homogeneous subspaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {261--265},
     publisher = {mathdoc},
     volume = {116},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2024_116_2_a7/}
}
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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/