Metrizability of spaces and weak base g-functions

On the Metrizability of Spaces with a Sharp Base

A base B for a space X is said to be sharp if, whenever x ∈ X and (Bn)n∈ω is a sequence of pairwise distinct elements of B each containing x, the collection { ⋂ j≤n Bj : n ∈ ω} is a local base at x. We answer questions raised by Alleche et al. and Arhangel’skĭı et al. by showing that a pseudocompact Tychonoff space with a sharp base need not be metrizable and that the product of a space with a ...

Metrizability of Decomposition Spaces

Simultaneous Metrizability of Coarse Spaces

A metric space can be naturally endowed with both a topology and a coarse structure. We examine the converse to this. Given a topology and a coarse structure we give necessary and sufficient conditions for the existence of a metric giving rise to both of these. We conclude with an application to the construction of the coarse assembly map.

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 ...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...