Complete metrizability of generalized compact-open topology

On fuzzy compact-open topology

The concept of fuzzy compact-open topology is introduced and some characterizations of this topology are discussed.

Resolvable Maps Preserve Complete Metrizability

Let X be a Polish space, Y a separable metrizable space, and f : X → Y a continuous surjection. We prove that if the image under f of every open set or every closed set is resolvable, then Y is Polish. This generalizes similar results by Sierpiński, Vainštain, and Ostrovsky.

Topology and Metrizability of Cone Metric Spaces

Abstract: Replacing the set of real numbers by an ordered Banach space in the definition of a metric, Guang and Xian [5] introduced the concept of a cone metric and obtained some fixed point Theorems for contractive mappings on cone metric spaces. It has been shown that every cone metric space is metrizable [2-4]. In this paper we review and simplify some results of [6] and as a consequence of ...

Compact Open Topology and Cw Homotopy Type

Sequential Properties of Function Spaces with the Compact-open Topology

Let M be the countably infinite metric fan. We show that Ck(M, 2) is sequential and contains a closed copy of Arens space S2. It follows that if X is metrizable but not locally compact, then Ck(X) contains a closed copy of S2, and hence does not have the property AP. We also show that, for any zero-dimensional Polish space X, Ck(X, 2) is sequential if and only if X is either locally compact or ...