Vesko Valov
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Vesko Valov has a total of 34 co-authors. Here are the top co-authors by number of shared publications:
- Alexandre Karassev
Nipissing University
5 shared publications - Alex Chigogidze
Department of Mathematical Sciences, University of North Carolina at Greensboro, PO Box 26170, Greensboro, NC 27402-6170, USA
4 shared publications - Andrzej Kucharski
Univ Silesia Katowice, Inst Math, Bankowa 14, PL-40007 Katowice, Poland
4 shared publications - E. Shchepin
Russian Acad Sci, Steklov Math Inst, 8 Gubkina St, Moscow 119991, Russia
4 shared publications - Jan van Mill
University of Amsterdam
4 shared publications A. Karasev
Nipissing University
3 shared publications
Latest Publications
- Open Access
- 25 September 2025
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- p. 1-22
On uniformly continuous surjections between function spaces
We consider uniformly continuous surjections between $C_p(X)$ and $C_p(Y)$ (resp., $C_p^*(X)$ and $C_p^*(Y$ )) and show that if X has some dimensional-like properties, then so does Y . In particular, we prove that if $T:C_p(X)\to C_p(Y)$ is a continuous linear surjection and $\dim X=0$ , then ${\dim Y=0}$ . This provides a positive answer to a question raised by Kawamura–Leiderman [11, Problem 3.1].- 25 September 2025
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- p. 1-22
Open AccessOn uniformly continuous surjections between function spaces
We consider uniformly continuous surjections between $C_p(X)$ and $C_p(Y)$ (resp., $C_p^*(X)$ and $C_p^*(Y$ )) and show that if X has some dimensional-like properties, then so does Y . In particular, we prove that if $T:C_p(X)\to C_p(Y)$ is a continuous linear surjection and $\dim X=0$ , then ${\dim Y=0}$ . This provides a positive answer to a question raised by Kawamura–Leiderman [11, Problem 3.1]. - Open Access
Homology manifolds and homogeneous compacta
A non-trivial separable metric space $X$ is called an almost homology $n$-manifold if the homology groups $H_k(X,X\backslash\{x\},\mathbb Z)$ are trivial for all $x\in X$ and all $k=0,1,..,n-1$. We provide a necessary and sufficient condition locally compact homogeneous $ANR$-spaces or strongly locally homogeneous $ANR$-spaces to be almost homology $n$-manifolds.Open AccessHomology manifolds and homogeneous compacta
A non-trivial separable metric space $X$ is called an almost homology $n$-manifold if the homology groups $H_k(X,X\backslash\{x\},\mathbb Z)$ are trivial for all $x\in X$ and all $k=0,1,..,n-1$. We provide a necessary and sufficient condition locally compact homogeneous $ANR$-spaces or strongly locally homogeneous $ANR$-spaces to be almost homology $n$-manifolds. - Open Access
- 17 October 2024
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 378 (2) , 1449-1463
Local structure of homogeneous 𝐴𝑁𝑅-spaces
We investigate to what extend finite-dimensional homogeneous locally compact A N R ANR -spaces have common properties with topological manifolds. Specially, the local structure of homogeneous A N R ANR -spaces is described. Using that description, we provide a positive solution of the problem whether every finite-dimensional homogeneous metric A N R ANR -compactum X X is dimensionally full-valued, i.e. dim X × Y = dim X + dim Y \dim X\times Y=\dim X+\dim Y for any metric compactum Y Y .
- 17 October 2024
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 378 (2) , 1449-1463
Open AccessLocal structure of homogeneous 𝐴𝑁𝑅-spaces
We investigate to what extend finite-dimensional homogeneous locally compact A N R ANR -spaces have common properties with topological manifolds. Specially, the local structure of homogeneous A N R ANR -spaces is described. Using that description, we provide a positive solution of the problem whether every finite-dimensional homogeneous metric A N R ANR -compactum X X is dimensionally full-valued, i.e. dim X × Y = dim X + dim Y \dim X\times Y=\dim X+\dim Y for any metric compactum Y Y .
- 24 March 2024
- Published by Elsevier in Topology and its Applications
- Vol. 348
Strongly locally homogeneous generalized continua of finite cohomological dimension
- 24 March 2024
- Published by Elsevier in Topology and its Applications
- Vol. 348
Strongly locally homogeneous generalized continua of finite cohomological dimension
- Open Access
- 5 March 2024
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society, Series B
- Vol. 11 (4) , 36-46
Separation of homogeneous connected locally compact spaces
We prove that any region Γ \Gamma in a homogeneous n n -dimensional and locally compact separable metric space X X , where n ≥ 2 n\geq 2 , cannot be irreducibly separated by a closed ( n − 1 ) (n-1) -dimensional subset C C with the following property: C C is acyclic in dimension n − 1 n-1 and there is a point b ∈ C ∩ Γ b\in C\cap \Gamma having a special local base B C b \mathcal B_C^b in C C such that the boundary of each U ∈ B C b U\in \mathcal B_C^b is acyclic in dimension n − 2 n-2 . In case X X is strongly locally homogeneous, it suffices to have a point b ∈ C ∩ Γ b\in C\cap \Gamma with an ordinary base B C b \mathcal B_C^b satisfying the above condition. The acyclicity means triviality of the corresponding Čech cohomology groups. This implies all known results concerning the separation of regions in homogeneous connected locally compact spaces.
- 5 March 2024
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society, Series B
- Vol. 11 (4) , 36-46
Open AccessSeparation of homogeneous connected locally compact spaces
We prove that any region Γ \Gamma in a homogeneous n n -dimensional and locally compact separable metric space X X , where n ≥ 2 n\geq 2 , cannot be irreducibly separated by a closed ( n − 1 ) (n-1) -dimensional subset C C with the following property: C C is acyclic in dimension n − 1 n-1 and there is a point b ∈ C ∩ Γ b\in C\cap \Gamma having a special local base B C b \mathcal B_C^b in C C such that the boundary of each U ∈ B C b U\in \mathcal B_C^b is acyclic in dimension n − 2 n-2 . In case X X is strongly locally homogeneous, it suffices to have a point b ∈ C ∩ Γ b\in C\cap \Gamma with an ordinary base B C b \mathcal B_C^b satisfying the above condition. The acyclicity means triviality of the corresponding Čech cohomology groups. This implies all known results concerning the separation of regions in homogeneous connected locally compact spaces.
- Open Access
Homogeneous locally compact spaces
This is a survey of the recent results and unsolved problems about locally compact homogeneous metric spaces. Mostly, homogeneous finite-dimensional $ANR$-spaces are discussed.
Open AccessHomogeneous locally compact spaces
This is a survey of the recent results and unsolved problems about locally compact homogeneous metric spaces. Mostly, homogeneous finite-dimensional $ANR$-spaces are discussed.
- Open Access
Separation of homogeneous connected locally compact spaces
We prove that any region $Γ$ in a homogeneous $n$-dimensional and locally compact separable metric space $X$, where $n\geq 2$, cannot be irreducibly separated by a closed $(n-1)$-dimensional subset $C$ with the following property: $C$ is acyclic in dimension $n-1$ and there is a point $b\in C\capΓ$ having a special local base $\mathcal B_C^b$ in $C$ such that the boundary of each $U\in\mathcal B_C^b$ is acyclic in dimension $n-2$. In case $X$ is strongly locally homogeneous, it suffices to have a point $b\in C\capΓ$ with an ordinary base $\mathcal B_C^b$ satisfying the above condition. The acyclicity means triviality of the corresponding Čech cohomology groups. This implies all known results concerning the separation of regions in homogeneous connected locally compact spaces.Open AccessSeparation of homogeneous connected locally compact spaces
We prove that any region $Γ$ in a homogeneous $n$-dimensional and locally compact separable metric space $X$, where $n\geq 2$, cannot be irreducibly separated by a closed $(n-1)$-dimensional subset $C$ with the following property: $C$ is acyclic in dimension $n-1$ and there is a point $b\in C\capΓ$ having a special local base $\mathcal B_C^b$ in $C$ such that the boundary of each $U\in\mathcal B_C^b$ is acyclic in dimension $n-2$. In case $X$ is strongly locally homogeneous, it suffices to have a point $b\in C\capΓ$ with an ordinary base $\mathcal B_C^b$ satisfying the above condition. The acyclicity means triviality of the corresponding Čech cohomology groups. This implies all known results concerning the separation of regions in homogeneous connected locally compact spaces. - Open Access
On generalized $V^n$-continua
The notion of a $V^n$-continuum was introduced by Alexandroff \cite{ps} as a generalization of the concept of $n$-manifold. In this note we consider the cohomological analogue of $V^n$-continuum and prove that any strongly locally homogeneous generalized continuum $X$ with cohomological dimension $\dim_G X=n$ is a generalized $V^n$-space with respect to the cohomological dimension $\dim_G$. In particular, every strongly locally homogeneous continuum of covering dimension $n$ is a $V^n$-continuum in the sense of Alexandroff. This provides a partial answer to a question raised in \cite{tv}. An analog of the Mazurkiewicz theorem that no subset of covering dimension $\le n-2$ cuts any region of the Euclidean $n$-space is also obtained for strongly locally homogeneous generalized continua $X$ of cohomological dimension $\dim_G X=n$.Open AccessOn generalized $V^n$-continua
The notion of a $V^n$-continuum was introduced by Alexandroff \cite{ps} as a generalization of the concept of $n$-manifold. In this note we consider the cohomological analogue of $V^n$-continuum and prove that any strongly locally homogeneous generalized continuum $X$ with cohomological dimension $\dim_G X=n$ is a generalized $V^n$-space with respect to the cohomological dimension $\dim_G$. In particular, every strongly locally homogeneous continuum of covering dimension $n$ is a $V^n$-continuum in the sense of Alexandroff. This provides a partial answer to a question raised in \cite{tv}. An analog of the Mazurkiewicz theorem that no subset of covering dimension $\le n-2$ cuts any region of the Euclidean $n$-space is also obtained for strongly locally homogeneous generalized continua $X$ of cohomological dimension $\dim_G X=n$. - 20 September 2023
- Published by Elsevier in Topology and its Applications
- Vol. 340
Extending homeomorphisms on Cantor cubes
- 20 September 2023
- Published by Elsevier in Topology and its Applications
- Vol. 340
Extending homeomorphisms on Cantor cubes
- Open Access
Proper absolute extensors
We describe the proper absolute (neighborhood) extensors for the class of at most $n$-dimensional spaces, notation $\rm{A(N)E}_p(n)$. For example, the unique locally compact $n$-dimensional separable metric space $X\in\rm{AE}_p(n)$ satisfiyng the $\rm{DD^nP}$-property is the $n$-dimensional Menger compactum without a point. Non-metrizable $\rm{A(N)E}_p(n)$-spaces are also described.Open AccessProper absolute extensors
We describe the proper absolute (neighborhood) extensors for the class of at most $n$-dimensional spaces, notation $\rm{A(N)E}_p(n)$. For example, the unique locally compact $n$-dimensional separable metric space $X\in\rm{AE}_p(n)$ satisfiyng the $\rm{DD^nP}$-property is the $n$-dimensional Menger compactum without a point. Non-metrizable $\rm{A(N)E}_p(n)$-spaces are also described.