Abstract
This article presents a new kind of class of all after composed set and fore composed set using the arbitrary binary relation based on nano topological space. We express the notion of nano equality, and nano inclusion and nano power set regarding binary relation based on nano topology. Also, we discuss their properties. Finally, the real life application of network topology is studied.
Highlights
Thivagar and Richard [1] introduced a nano topological space with respect to a subset X of an universe, which is defined in terms of lower and upper approximations and boundary region of X
We express the notion of nano equality, and nano inclusion and nano power set regarding binary relation based on nano topology
This paper systematically studied that any kind of binary relation can be used to relational topology induced by nano topological space
Summary
Thivagar and Richard [1] introduced a nano topological space with respect to a subset X of an universe, which is defined in terms of lower and upper approximations and boundary region of X. This paper introduces and defines a new type of class of all after-composed set and the class of all fore composed set denoted by τ R and Rτ and used in nano topological space induced by any binary relation. Some of their properties are studied and investigated. We show the differences and relationships between the notions of ordinary set theory and nano topological space. We present the application of network topology [2] in nano topology
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