A5019822589- Homotopy and Cohomology in Algebraic Topology
- Geometric and Algebraic Topology
- Advanced Topology and Set Theory
- Advanced Operator Algebra Research
- Advanced Topics in Algebra
- Algebraic structures and combinatorial models
- Topological and Geometric Data Analysis
- Mathematical Dynamics and Fractals
- Advanced Banach Space Theory
- Mathematics and Applications
- Geometric Analysis and Curvature Flows
- Advanced Numerical Analysis Techniques
- Holomorphic and Operator Theory
- Algebraic Geometry and Number Theory
- Geometry and complex manifolds
- Advanced Algebra and Geometry
- Ophthalmology and Eye Disorders
- History and Theory of Mathematics
- Intracranial Aneurysms: Treatment and Complications
- Advanced Differential Geometry Research
- Rings, Modules, and Algebras
- Advanced Algebra and Logic
- Computational Geometry and Mesh Generation
- Optics and Image Analysis
- Limits and Structures in Graph Theory
University of Tennessee at Knoxville
2010-2023
Xi'an Technological University
2023
University of Ljubljana
2012
Institute of Mathematics, Physics, and Mechanics
2012
Utah State University
1992
Institute of Mathematics
1988-1991
University of Warsaw
1982-1991
University of California, Riverside
1988
University of Washington
1978-1988
Auburn University
1988
Given a function f : X → Y of metric spaces, its asymptotic dimension asdim(f ) is the supremum asdim(A) such that A ⊂ and (A)) = 0. Our main result Theorem 0.1.asdim(X) ≤ + asdim(Y for any large scale uniform .0.1 generalizes Bell Dranishnikov [3] in which Lipschitz geodesic.We provide analogs 0.1 Assouad-Nagata dim AN asdim .In case linearly controlled l-asdim we counterexamples to three questions [14].As an application provean exact sequence groups G finitely generated, then (G, d (K, |K)...
We define Peano covering maps and prove basic properties analogous to classical covers. Their domain is always locally path-connected but the range may be an arbitrary topological space. One of characterizations via uniq
The purpose of this paper is to address several problems posed by V. I. Kuzminov [Ku] regarding cohomological dimension noncompact spaces.In particular, we prove the following results:
The paper deals with generalizing several theorems of the covering dimension theory to extension separable metrizable spaces. Here are some main results: Generalized Eilenberg-Borsuk Theorem. Let $L$ be a countable CW complex. If $X$ is space and $K\ast L$ an absolute extensor for complex $K$, then any map $f:A\to K$, $A$ closed in $X$, there $f':U\to K$ $f$ over open set $U$ such that $L\in AE(X-U)$. $K,L$ complexes. subset $Y$ $K\in AE(Y)$ AE(X-Y)$. Suppose $G_{i},\ldots ,G_{n}$ countable,...
We prove that the dimension of any asymptotic cone over a metric space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper X comma rho right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>ρ</mml:mi> stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">(X,\rho )</mml:annotation> </mml:semantics> </mml:math>...
We discuss various uniform structures and topologies on the universal covering space $\widetilde X$ fundamental group $π_1(X,x_0)$. introduce a canonical structure $CU(X)$ topological $X$ use it to relate $\widetilde{CU(X)}$. Using our concept of Peano we show connections between topology introduced by Spanier Berestovskii Plaut. give sufficient necessary condition for Berestovskii-Plaut be identical with one generated convergence paths in $X$. also describe when is quotient compact-open paths.
This paper is devoted to dualization of paracompactness the coarse category via concept $R$ -disjointness. Property A Yu can be seen as a variant amenability partitions unity and leads unity. On other hand, finite decomposition complexity Guentner, Tessera, straight Dranishnikov Zarichnyi employ -disjointness main concept. We generalize both concepts that countable asymptotic dimension our result shows it subclass spaces with A. In addition, gives necessary sufficient condition for dimension.
The main result of the first part paper is a generalization classical Menger-Urysohn : $\dim (A\cup B)\le \dim A+\dim B+1$. Theorem. Suppose $A,B$ are subsets metrizable space and $K$ $L$ CW complexes. If an absolute extensor for $A$ $B$, then join $K*L$ $A\cup B$. As application we prove following analogue Theorem cohomological dimension: $A$, $B$ space. Then \begin{equation*}\dim _{\mathbf {R} }(A\cup }A+\dim }B+1 \end{equation*} any ring $\mathbf {R}$ with unity _{G}(A\cup _{G}A+\dim...
Examples are constructed that include: first, a separable metric space having cohomological dimension 4 such every Hausdorff compactification has at least 5; second, locally compact whose Stone-Čech infinite dimension.
Abstract Consider the wreath product H ≀ G , where ≠ 1 is finite and finitely generated. We show that Assouad–Nagata dimension dim AN (H ) of depends on growth as follows: if not bounded by a linear function, then ( G) = ∞; otherwise ≤ 1.
The main results of the paper are following: <bold>Theorem.</bold> <italic>Suppose</italic> <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n less-than-or-equal-to normal infinity"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mi mathvariant="normal">∞<!-- ∞ --></mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">n \leq \infty</mml:annotation> </mml:semantics> </mml:math>...
Strong shape equivalences for topological spaces are introduced in a way which generalizes easily to inverse systems of spaces. Each space is then mapped via strong equivalence into fibrant system ANRs. This leads naturally defining the category SSh Other descriptions also provided.