Function valued metric spaces
Journal Title: Surveys in Mathematics and its Applications - Year 2010, Vol 5, Issue 0
Abstract
In this paper we introduce the notion of an &#8497;-metric, as a function valued distance mapping, on a set X and we investigate the theory of &#8497;-metrics paces. We show that every metric space may be viewed as an &#8497;-metric space and every &#8497;-metric space (X,δ) can be regarded as a topological space (X,τ<SUB>δ</SUB>). In addition, we prove that the category of the so-called extended &#8497;-metric spaces properly contains the category of metric spaces. We also introduce the concept of an <FONT FACE="Symbol">`</FONT>&#8497;-metric space as a completion of an &#8497;-metric space and, as an application to topology, we prove that each normal topological space is <FONT FACE="Symbol">`</FONT>&#8497;-metrizable.
Authors and Affiliations
Madjid Mirzavaziri
Keywords
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