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pro vyhledávání: '"Karassev, Alexandre"'
This is a survey of recent and classical results concerning various types of homogeneity, such as n-homogeneity, discrete homogeneity, and countable dense homogeneity. Some new results are also presented, and several problems are posed.
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Externí odkaz:
http://arxiv.org/abs/2407.11815
Autor:
Karassev, Alexandre, Valov, Vesko
It was shown by van Mill and Valov that regions in strongly locally homogeneous locally compact metric spaces of dimension $\ge 2$ are not separated by arcs. We improve this result by replacing strong local homogeneity with homogeneity. Moreover, we
Externí odkaz:
http://arxiv.org/abs/2302.06735
It is shown that a connected non-compact metrizable manifold of dimension $\ge 2$ is strongly discrete homogeneous if and only if it has one end (in the sense of Freudenthal compactification).
Externí odkaz:
http://arxiv.org/abs/2210.04978
Autor:
Chatyrko, Vitaly, Karassev, Alexandre
We introduce the classes of (strongly) ($\Theta$-)discrete homogeneous spaces. We discuss the relationships of these classes to other classes of spaces possessing homogeneity-related properties, such as (strongly) ($n$-)homogeneous spaces. Many examp
Externí odkaz:
http://arxiv.org/abs/2208.00506
Autor:
Karassev, Alexandre, Valov, Vesko
We investigate to what extend the density of $Z_n$-maps in the characterization of $Q$-manifolds, and the density of maps $f\in C(\mathbb N\times Q,X)$ having discrete images in the $l_2$-manifolds characterization can be weakened to the density of h
Externí odkaz:
http://arxiv.org/abs/2012.00231
Publikováno v:
In Topology and its Applications 15 August 2023 336
Autor:
Karassev, Alexandre V.
There is a new approach in dimension theory, proposed by A. N. Dranishnikov and based on the concept of extension types of complexes. Following Dranishnikov, for a CW-complex L we introduce the definition of extension type [L] of this complex. Fu
We prove the following result announced in Todorov and Valov: Any homogeneous, metric $ANR$-continuum is a $V^n_G$-continuum provided $\dim_GX=n\geq 1$ and $\check{H}^n(X;G)\neq 0$, where $G$ is a principal ideal domain. This implies that any homogen
Externí odkaz:
http://arxiv.org/abs/1208.6345
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Publikováno v:
Mathematica Slovaca; Dec2023, Vol. 73 Issue 6, p1587-1596, 10p