Open AccessInvestigation of topological spaces using relators
Author(s) -
Gergely Pataki
Publication year - 2022
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2022.16128
Subject(s) - mathematics , axiom , property (philosophy) , topological space , topology (electrical circuits) , network topology , separation axiom , pure mathematics , discrete mathematics , combinatorics , computer science , epistemology , geometry , operating system , philosophy
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.