Some Methods for Generating Topologies by Relations

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 universes. 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