%0 Journal Article
%T Function valued metric spaces
%A Madjid Mirzavaziri
%J Surveys in Mathematics and its Applications
%D 2010
%I University Constantin Brancusi of Targu-Jiu
%X In this paper we introduce the notion of an  -metric, as a function valued distance mapping, on a set X and we investigate the theory of  -metrics paces. We show that every metric space may be viewed as an F-metric space and every  -metric space (X,¦Ä) can be regarded as a topological space (X,¦Ó¦Ä). 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 ` -metric space as a completion of an  -metric space and, as an application to topology, we prove that each normal topological space is ` -metrizable.
%K Function valued metric
%K Positive element
%K Strictly positive element
%K -completeness
%K -metric space
%K Allowance set
%K -Cauchy
%K -completion
%K -metrizable
%U http://www.utgjiu.ro/math/sma/v05/p24.pdf