Some methods for generating topologies by relations.
Malaysian Mathematical, A.A. Allam, M. Y. Bakeir, El-Sayed A. Abo-Tabl · 2008
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.