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.
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/
@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},
year = {2024},
volume = {116},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2024_116_2_a7/}
}
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