Geodesic
Some Methods for Generating Topologies by Relations
Bulletin of the Malaysian Mathematical Society, Tome 31 (2008) no. 1 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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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.
Classification : 04A05, 54A05. 
@article{BMMS_2008_31_1_a3,
     author = {A. A. Allam and M. Y. Bakeir and E. A. Abo-Tabl},
     title = {Some {Methods} for {Generating} {Topologies} by {Relations}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2008},
     volume = {31},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2008_31_1_a3/}
}
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A. A. Allam; M. Y. Bakeir; E. A. Abo-Tabl. Some Methods for Generating Topologies by Relations. Bulletin of the Malaysian Mathematical Society, Tome 31 (2008) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2008_31_1_a3/