The Metrizable Linear Extensions of Metrizable Sets in Topological Linear Spaces

Proto-metrizable fuzzy topological spaces

Equivariant Embedding of Metrizable G-spaces in Linear G-spaces

Given a Lie group G we study the class MG of proper metrizable G-spaces with metrizable orbit spaces, and show that any G-space X ∈ MG admits a closed G-embedding into a convex G-subset C of some locally convex linear G-space, such that X has some G-neighborhood in C which belongs to the class MG. As a corollary we see that any G-ANR for MG is a G-ANE for MG.

Basic Properties of Metrizable Topological Spaces

We continue Mizar formalization of general topology according to the book [16] by Engelking. In the article, we present the final theorem of Section 4.1. Namely, the paper includes the formalization of theorems on the correspondence between the cardinalities of the basis and of some open subcover, and a discreet (closed) subspaces, and the weight of that metrizable topological space. We also de...

- 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 ...

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...