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This work focuses on rough approximation operators generated from milli topological spaces and examines their features. For this purpose, we show how milli continuous functions are constructed. Further, exploiting the concepts of milli contra continuous, milli perfectly continuous, milli strongly continuous functions and milli basis in milli topological spaces, a real-life application is presented. The essential food habits for a healthy lifestyle were identified. Here the concepts of the topological reduction of attributes in a complete information system is used to get the key factors. A general algorithm for identifying the key factors is provided. [ABSTRACT FROM AUTHOR]

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This paper aims to introduce the concept of nano α- derived set and study the characteristics of nano α- derived set. Further, we investigate the different forms of nano α- derived set using lower and upper approximation. [ABSTRACT FROM AUTHOR]

This article presents a new formulation of nano toplogical structure for a given ideal. The choice of the ideal has its own impact on the nano approximations. Also we discuss some of their properties and a comparative analysis have been done based on nano approximations..The nano approximations via ideal results in diminished upper approximation, enlarged lower approximation and elevated accuracy. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce an operator γ, a function from N-BO(U) ! P(U) in nano topological space (U,TR(X)). Here we have also characterised various properties based on the operation γ. Moreover we have made an attempt to develop some new spaces through Nγb open sets in nano topological space and finally we have also examined the relationship among them. [ABSTRACT FROM AUTHOR]

The prime aim of this paper is to introduce some new type of sets in grill N-topologies and subsequently establish that such collections of sets satisfy the topological axioms. We further develop the continuous and irresolute functions by using the weak forms of grill open sets. Finally, we derive the composition of such functions with suitable examples. [ABSTRACT FROM AUTHOR]

This work is devoted to conformal dynamics in metric spaces, it consists of two parts, the first concerning hyperbolic groups, and the second is the iteration of branched coatings in topological spaces. These two parts are linked by D. Sullivan's dictionary. We chose to orient the exhibition taking the conjecture of J. W. Cannon as breadcrumb. The object of this work has been to analyze these different methods to understand to what extent they were different than D. Sullivan [28]. [ABSTRACT FROM AUTHOR]

By introducing the topological generalized closed sets into Ntopological space, this paper establishes that the union of τi-generalized closed sets need not be Nτ -generalized closed set. Further, the collection of Nτ - g closed sets form a topology. Apart from this, Nτ - g closed sets are characterized by means of Nτ#gs-kernel. [ABSTRACT FROM AUTHOR]

The aim of this paper is to evolve a nano topological structure from a finite group and here we define the nano approximations via normal subgroup of a group and its properties were also discussed based on choice of Normal sub-groups. Algebraically and topologically, structural equivalences are based on the two renowned maps isomorphism between groups and homeomorphism in topolog-ical spaces. This induces us to create a link between groups and Nano topology induced by group which in turn has its own impact on well known theorems such as Fundamental theorem of homomorphism on groups and Second isomorphism theorem. [ABSTRACT FROM AUTHOR]

The objective of this paper is to define nano hyper connected space and study its properties.This paper gives a charcterization of nano hyper connected spaces,using the concept of nano pre open sets and nano semi open sets. Further some new weak nano functions are defined which preserve nano hyperconnected property. [ABSTRACT FROM AUTHOR]

This paper deals with an approximation space and a hypergroup theory. Also we introduce invertible subhypergroup nano topology. Moreover, the notion of a normal and closed subhypergroup gives the characterization of invertible subhypergroup nano topology. Finally, we have shown that copper has same crystalline form but different chemical composition using nano homeomorphic in invertible subhypergroup nano topology. [ABSTRACT FROM AUTHOR]

The main objective of this study is to introduce a new hybrid intelligent structure called Neutrosophic nano topology. Fuzzy nano topology and intuitionistic nano topology can also be deduced from the neutrosophic nano topology. Based on the neutrosophic nano approximations we have classified neutrosophic nano topology. Some properties like neutrosophic nano interior and neutrosophic nano closure are derived. [ABSTRACT FROM AUTHOR]

In this paper we desire to extend the neutrosophic topological spaces into N-neutrosophic topological spaces. Also we show that this theory can be deduced to N-intuitionistic and N-fuzzy topological spaces etc. Further we develop not only the concept of classical generalized closed sets into N-neutrosophic topological spaces but also obtain its basic properties. Finally we investigate its continuous function and generalized continuous function. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a new method of nano topological space stimulated by soft set. The soft set is generated in lower approximation, upper approximation and boundary region, called as "Nano Soft Topological Space(NSTS)". We study the properties of soft approximation space (U; FA) in NSTS. Further, we de ne with an example a new soft matrices induced by binary relation through the NSTS. To study the real life application, we carried out an comparative analysis between nano topological space and NSTS induced by soft matrix. [ABSTRACT FROM AUTHOR]