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What is a relator space?

Topological space

Space (mathematics)

Property (philosophy)

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A relator space is a mathematical concept defined by a family of binary relations on a set, where the ordered pair represents the relator space itself. These spaces provide a framework for studying various continuity properties and topological structures. They allow for the derivation of generalized topologies and the definition of essential operations like closure, interior, and boundary. Relator spaces have been used to define uniformities, proximities, and topologies, showing equivalences with classical definitions and enabling comparisons between different topological structures. The study of relator spaces has attracted significant attention from mathematicians due to their utility in investigating continuity-like properties and relationships between different spaces.

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Open access•Journal Article•DOI Investigation of topological spaces using relators Gergely Pataki 01 Apr 2022-Applied general topology 1 Citations	A relator space is defined using uniformities and topologies, showing equivalence with classical definitions. It allows for comparing different topological structures in new ways.
Open access•Journal Article•DOI Investigation of Proximal Spaces Using Relators Gergely Pataki 30 Jun 2021 2 Citations	A relator space defines uniformities and proximities, showing equivalence with classical definitions. It summarizes essential properties and introduces uniformly and proximally filtered properties.
Open access Characterizations of Generalized Topologically Open Sets in Relator Spaces Themistocles M. Rassias, Muwafaq M. Salih, Árpád Száz - Show less +2 more 25 Apr 2021 1 Citations	A relator space is an ordered pair consisting of a set and a family of binary relations on that set, allowing for the derivation of generalized topologies.
Journal Article•DOI Contra Continuity Properties of Relations in Relator Spaces Bryan Muller 01 Jan 2023-Industrial and applied mathematics	A relator space is an ordered pair $(X(\mathscr {R})=(X, \mathscr {R})$ consisting of a set X and a family of relations $\mathscr {R}$ on X, serving as a generalization of ordered sets and uniform spaces.
Book Chapter•DOI A General Framework for Studying Certain Generalized Topologically Open Sets in Relator Spaces Themistocles M. Rassias, Árpád Száz - Show less +1 more 01 Jan 2021 1 Citations	A relator space is an ordered pair \( X(\mathcal {R})=( X, \mathcal {R})\) where \(\mathcal {R}\) is a family of binary relations on set X, used for studying generalized topologically open sets.

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