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 ℱ-metric, as a function valued distance mapping, on a set X and we investigate the theory of ℱ-metrics paces. We show that every metric space may be viewed as an ℱ-metric space and every ℱ-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 ℱ-metric spaces properly contains the category of metric spaces. We also introduce the concept of an <FONT FACE="Symbol">`</FONT>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 <FONT FACE="Symbol">`</FONT>ℱ-metrizable.

Authors and Affiliations

Madjid Mirzavaziri

Keywords

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  • EP ID EP129498
  • DOI -
  • Views 97
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How To Cite

Madjid Mirzavaziri (2010). Function valued metric spaces. Surveys in Mathematics and its Applications, 5(0), 321-332. https://europub.co.uk/articles/-A-129498