Cohomological dimension and metrizable spaces. II

On D-dimension of metrizable spaces*

For every cardinal τ and every ordinal α, we construct a metrizable space Mα(τ) and a strongly countable-dimensional compact space Zα(τ) of weight τ such that D(Mα(τ)) ≤ α, D(Zα(τ)) ≤ α and each metrizable space X of weight τ such that D(X) ≤ α is homeomorphic to a subspace of Mα(τ) and to a subspace of Zα+1(τ).

Cohomological Dimension Theory of Compact Metric Spaces

0. Introduction 1 1. General properties of the cohomological dimension 2 2. Bockstein theory 6 3. Cohomological dimension of Cartesian product 10 4. Dimension type algebra 15 5. Realization theorem 19 6. Test spaces 24 7. Infinite-dimensional compacta of finite cohomological dimension 28 8. Resolution theorems 33 9. Resolutions preserving cohomological dimensions 41 10. Imbedding and approximat...

- Metrizable Spaces and Their Applications

In this paper we introduce and study so-called k∗-metrizable spaces forming a new class of generalized metric spaces, and display various applications of such spaces in topological algebra, functional analysis, and measure theory. By definition, a Hausdorff topological space X is k∗-metrizable if X is the image of a metrizable space M under a continuous map f : M → X having a section s : X → M ...

Proto-metrizable fuzzy topological spaces

Continuity in Separable Metrizable and Lindelöf Spaces

Given a map T : X → X on a set X we examine under what conditions there is a separable metrizable or an hereditarily Lindelöf or a Lindelöf topology on X with respect to which T is a continuous map. For separable metrizable and hereditarily Lindelöf, it turns out that there is a such a topology precisely when the cardinality ofX is no greater than the cardinality of the continuum. We go onto pr...