Closed maps and spaces with zero-dimensional remainders

Closed Maps and the Character of Spaces

We give some necessary and sufficient conditions for the character of spaces to be preserved under closed maps. Introduction. Recall the following result due to K. Morita and S. Hanai [11] or A. H. Stone [14]: Let Y be the image of a metric space X under a closed map/. Then Y is first countable (or metrizable) if and only if every boundary df~x(y) of the point-inverse/"'^) is compact. E. Michae...

Zero - Entropy Affine Maps on Homogeneous Spaces

A Note on Closed Subsets in Quasi-zero-dimensional Qcb-spaces

We introduce the notion of quasi-zero-dimensionality as a substitute for the notion of zero-dimensionality, motivated by the fact that the latter behaves badly in the realm of qcb-spaces. We prove that the category QZ of quasi-zero-dimensional qcb0-spaces is cartesian closed. Prominent examples of spaces in QZ are the spaces of the Kleene-Kreisel continuous functionals equipped with the respect...

A Note on Closed Subsets in Quasi-zero-dimensional Qcb-spaces (Extended Abstract)

We introduce the notion of quasi-zero-dimensionality as a substitute for the notion of zero-dimensionality, motivated by the fact that the latter behaves badly in the realm of qcb-spaces. We prove that the category QZ of quasi-zero-dimensional qcb0-spaces is cartesian closed. Prominent examples of spaces in QZ are the spaces in the sequential hierarchy of the Kleene-Kreisel continuous functiona...

Topological entropy on zero-dimensional spaces

Let X be an uncountable compact metrizable space of topological dimension zero. Given any a ∈ [0,∞] there is a homeomorphism on X whose topological entropy is a.