Pseudo-completeness in linear metrizable 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.

Completeness in Probabilistic Metric Spaces

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...

Variational Principles and Completeness in Pseudo-Quasimetric Spaces

In this paper we establish new forward and backward versions of Ekeland’s variational principle for the class of strictly-decreasing forward(resp. backward-) lower-semicontinuou functionals in pseudo-quasimetric spaces. We do not require that the space under consideration either is complete or enjoys the limit uniqueness property due to the fact that the collections of forward and backward limi...

- 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