Investigation of topological spaces using relators

Gergely Pataki

doi:10.4995/agt.2022.16128

Authors

Gergely Pataki Budapest University of Technology and Economics https://orcid.org/0000-0002-4630-9949

DOI:

https://doi.org/10.4995/agt.2022.16128

Keywords:

(generalized) uniformities, (generalized) topologies, relators

Abstract

In this paper, we define uniformities and topologies as relators and show the equivalences of these definitions with the 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 show that our earlier analogous definition [G. Pataki, Investigation of proximal spaces using relators, Axioms 10, no. 3 (2021): 143.] for uniformly and proximally filtered property is equivalent to the topological one.

At the end of this paper, uniformities and topologies are defined in the same way. This will give us new possibilities to compare these and other topological structures.

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Author Biography

Gergely Pataki, Budapest University of Technology and Economics

Department of Analysis (BUTE) ; Department of Mathematics and Modelling, Hungarian University of Agriculture and Life Sciences

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