Some methods for generating topologies by relations.

Malaysian Mathematical · A.A. Allam · M. Y. Bakeir · El-Sayed A. Abo-Tabl

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Fuzzy and Soft Set Theory Advanced Topology and Set Theory Rough Sets and Fuzzy Logic

Abstract

Relation on a set is a simple mathematical model to which many real-life data can be connected. In fact, topological structures are generalized methods for measuring similarity and dissimilarity between objects in the uni- verses. In this work, some methods for generating topologies are obtained using binary relations. The relationship between these methods are discussed. We also investigate some properties of these topologies. Moreover, we obtain a quasi-discrete topology from a symmetric relation instead of an equivalence relation. Finally, several examples are given to indicate counter connections.

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