Investigation of topological spaces using relators
Submitted: 2021-08-26
|Accepted: 2021-11-23
|Published: 2022-04-01
Copyright (c) 2022 Applied General Topology
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
(generalized) uniformities, (generalized) topologies, relators
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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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