Surveys in Mathematics and its Applications, Volume (5), No (5), Year (2010-5) , Pages (321-332)

Title : ( Function Valued Metric Spaces )

Authors: Madjid Mirzavaziri ,

Citation: BibTeX | EndNote

Abstract

In this paper we introduce the notion of an F-metric, as a function valued distance mapping, on a set X and we investigate the theory of F-metric spaces. We show that every metric space may be viewed as an F-metric space and every F-metric space (X, ) can be regarded as a topological space (X, ). In addition, we prove that the category of the so-called extended Fmetric spaces properly contains the category of metric spaces. We also introduce the concept of an F¯-metric space as a completion of an F-metric space and, as an application to topology, we prove that each normal topological space is F¯-metrizable.

Keywords

Function valued metric; Positive element; Strictly positive element
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@article{paperid:1018688,
author = {Mirzavaziri, Madjid},
title = {Function Valued Metric Spaces},
journal = {Surveys in Mathematics and its Applications},
year = {2010},
volume = {5},
number = {5},
month = {May},
issn = {1843-7265},
pages = {321--332},
numpages = {11},
keywords = {Function valued metric; Positive element; Strictly positive element},
}

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%0 Journal Article
%T Function Valued Metric Spaces
%A Mirzavaziri, Madjid
%J Surveys in Mathematics and its Applications
%@ 1843-7265
%D 2010

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