Investigation of Proximal Spaces Using Relators

Investigation of Proximal Spaces Using Relators

In this paper, we define uniformities and proximities as relators and show the equivalences of these definitions with classical ones. For this, we summarize the essential properties of relators, using their theory from earlier works of Á. Száz. Moreover, we prove implications between important topol...

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Bibliographic Details
Main Author: Gergely Pataki
Format: Article
Language:English
Published: MDPI AG 2021-06-01
Series:Axioms
Subjects:
(generalized) uniformities
(generalized) proximities
relators
Online Access:https://www.mdpi.com/2075-1680/10/3/143
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spelling doaj-84810cf4127c47b3a21072a18e7d7f222021-09-25T23:44:37ZengMDPI AGAxioms2075-16802021-06-011014314310.3390/axioms10030143Investigation of Proximal Spaces Using RelatorsGergely Pataki0Department of Mathematical Analysis, Budapest University of Technology and Economics, H1111 Budapest, HungaryIn this paper, we define uniformities and proximities as relators and show the equivalences of these definitions with classical ones. For this, we summarize the essential properties of relators, using their theory from earlier works of Á. Száz. Moreover, we prove implications between important topological properties of relators and disprove others. Finally, we add an analogous definition for uniformly and proximally filtered properties.https://www.mdpi.com/2075-1680/10/3/143(generalized) uniformities(generalized) proximitiesrelators
collection DOAJ
language English
format Article
sources DOAJ
author Gergely Pataki
spellingShingle Gergely Pataki
Investigation of Proximal Spaces Using Relators
Axioms
(generalized) uniformities
(generalized) proximities
relators
author_facet Gergely Pataki
author_sort Gergely Pataki
title Investigation of Proximal Spaces Using Relators
title_short Investigation of Proximal Spaces Using Relators
title_full Investigation of Proximal Spaces Using Relators
title_fullStr Investigation of Proximal Spaces Using Relators
title_full_unstemmed Investigation of Proximal Spaces Using Relators
title_sort investigation of proximal spaces using relators
publisher MDPI AG
series Axioms
issn 2075-1680
publishDate 2021-06-01
description In this paper, we define uniformities and proximities as relators and show the equivalences of these definitions with classical ones. For this, we summarize the essential properties of relators, using their theory from earlier works of Á. Száz. Moreover, we prove implications between important topological properties of relators and disprove others. Finally, we add an analogous definition for uniformly and proximally filtered properties.
topic (generalized) uniformities
(generalized) proximities
relators
url https://www.mdpi.com/2075-1680/10/3/143
work_keys_str_mv AT gergelypataki investigationofproximalspacesusingrelators
_version_ 1717368119604805632

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