-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.
Components and inductive dimensions of compact spaces
Compositions of simple maps
A map (= continuous function) is of order ≤ k if each of its point-inverses has at most k elements. Following [4], maps of order ≤ 2 are called simple. Which maps are compositions of simple closed [open, clopen] maps? How many simple maps are really needed to represent a given map? It is proved herein that every closed map of order ≤ k defined on an n-dimensional metric space is a composition of (n+1)k-1 simple closed maps (with metric domains). This theorem fails to be true...
Conditions which ensure that a simple map does not raise dimension
The present paper deals with those continuous maps from compacta into metric spaces which assume each value at most twice. Such maps are called here, after Borsuk and Molski (1958) and as in our previous paper (1990), simple. We investigate the possibility of decomposing a simple map into essential and elementary factors, and the so-called splitting property of simple maps which raise dimension. The aim is to get insight into the structure of those compacta which have the property that simple maps...
Constructive dimension theory
Continuous selections, -subsets of Banach spaces and usco mappings
Every l.s.cṁapping from a paracompact space into the non-empty, closed, convex subsets of a (not necessarily convex) -subset of a Banach space admits a single-valued continuous selection provided every such mapping admits a convex-valued usco selection. This leads us to some new partial solutions of a problem raised by E. Michael.
Correction to the paper: “Some factorization theorems for paracompact -spaces”