Approximable dimension and acyclic resolutions
Approximate inverse systems of uniform spaces and an application of inverse systems
The fundamental properties of approximate inverse systems of uniform spaces are established. The limit space of an approximate inverse sequence of complete metric spaces is the limit of an inverse sequence of some of these spaces. This has an application to the dimension of the limit space of an approximate inverse system. A topologically complete space with is the limit of an approximate inverse system of metric polyhedra of . A completely metrizable separable space with is the limit of an...
Asymptotic dimension of coarse spaces.
Bericht über einige neue Ergebnisse und Probleme auf dem Gebiet der anschaulichen Topologie.
Bing maps and finite-dimensional maps
Let X and Y be compacta and let f:X → Y be a k-dimensional map. In [5] Pasynkov stated that if Y is finite-dimensional then there exists a map such that dim (f × g) = 0. The problem that we deal with in this note is whether or not the restriction on the dimension of Y in the Pasynkov theorem can be omitted. This problem is still open. Without assuming that Y is finite-dimensional Sternfeld [6] proved that there exists a map such that dim (f × g) = 1. We improve this result of Sternfeld showing...
Borsuk-Sieklucki theorem in cohomological dimension theory
The Borsuk-Sieklucki theorem says that for every uncountable family of n-dimensional closed subsets of an n-dimensional ANR-compactum, there exist α ≠ β such that . In this paper we show a cohomological version of that theorem: Theorem. Suppose a compactum X is , where n ≥ 1, and G is an Abelian group. Let be an uncountable family of closed subsets of X. If for all α ∈ J, then for some α ≠ β. For G being a countable principal ideal domain the above result was proved by Choi and Kozlowski...
-spaces and simplicial complexes.
Cantor manifolds in the theory of transfinite dimension
For every countable non-limit ordinal α we construct an α-dimensional Cantor ind-manifold, i.e., a compact metrizable space such that , and no closed subset L of with ind L less than the predecessor of α is a partition in . An α-dimensional Cantor Ind-manifold can be constructed similarly.
Čech cohomology and covering dimension for topological spaces
Cell-like maps, dimension and cohomological dimension: a survey
Cell-like resolutions preserving cohomological dimensions.
Characterizations of uniformity-dependent dimension functions
Characterizing strong countable-dimensionality in terms of Baire category
Classification of weakly infinite-dimensional spaces. Part II: Essential mappings
Classification of weakly infinite-dimensional spaces. Part I: A transfinite extension of the covering dimension
Closed mappings and local dimension
Closed subgroups in Banach spaces
We show that zero-dimensional nondiscrete closed subgroups do exist in Banach spaces E. This happens exactly when E contains an isomorphic copy of . Other results on subgroups of linear spaces are obtained.
Coarse dimensions and partitions of unity.
Gromov and Dranishnikov introduced asymptotic and coarse dimensions of proper metric spaces via quite different ways. We define coarse and asymptotic dimension of all metric spaces in a unified manner and we investigate relationships between them generalizing results of Dranishnikov and Dranishnikov-Keesling-Uspienskij.
Cohomology, dimension and large Riemannian manifolds.
Colorings of Periodic Homeomorphisms
We calculate the exact value of the color number of a periodic homeomorphism without fixed points on a finite connected graph.