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
A Fuzzy Commitment Scheme with McEliece's Cipher
In this paper an attempt has been made to explain a fuzzy commitment scheme with McEliece scheme. The efficiency and security of this cryptosystem is comparatively better than any other cryptosystem. This scheme is one o...
Existence and uniqueness of the solution of the coupled conduction-radiation energy transfer on diffuse-gray surfaces
This article gives very significant and up-to-date analytical results on the conductive-radiative heat transfer model containing two conducting and opaque materials which are in contact by radiation through a transparent...
Optimal Alternative to the Akima's Method of Smooth Interpolation Applied in Diabetology
It is presented a new method of cubic piecewise smooth interpolation applied to experimental data obtained by glycemic profile for diabetics. This method is applied to create a soft useful in clinical diabetology. The me...
On certain Baskakov-Durrmeyer type operators
This paper is a study of the degree of approximation by the linear combinations of the derivatives of certain Durrmeyer type integral modification of the Baskakov operators in terms of the higher order modulus of smoothn...
On another two cryptographic identities in universal Osborn loops
In this study, by establishing an identity for universal Osborn loops, two other identities (of degrees 4 and 6) are deduced from it and they are recognized and recommended for cryptography in a similar spirit in which t...