Function Spaces of Completely Metrizable Spaces

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

- 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

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.

Irreducible representations of metrizable spaces and strongly countable-dimensional spaces

We generalize Freudenthal’s theory of irreducible representations of metrizable compacta by inverse sequences of compact polyhedra to the class of all metrizable spaces. Our representations consist of inverse sequences of completely metrizable polyhedra which are ANR’s. They are extendable: any such representation of a closed subspace of a given metrizable space extends to another such of the e...