The basic objective of this paper is to introduce and investigate the properties of nano semi pre-neighbourhoods, nano semi pre-interior, nano semi pre-frontier, nano semi pre-exterior, nano-dense, nano-submaximal and obtain relation between some of the existing sets. KeywordsNano β -interior, nano β -closure, nano β -neighbourhoods, nano β -frontier, nano β -exterior, nano-dense, nanosubmaximal.

The aim of this paper is to introduce the concept of generalized regular star closed sets and study some of its properties.

In this paper, we have introduce a new class of closed sets in topological spaces called θ-generalized star closed set (briefly θg*-closed set) and study some of its properties. Further we introduce the the concept of θg*-continuous functions, θg*-irresolute functions and contra θg*-continuous functions and study the relationship between other existing functions in topological spaces. Also we investigate the composition of the functions between θg*-continuous functions and between continuous and contra θg*-continuous functions and between θg*-continuous functions and

This paper focuses on N s g-closed sets (nano semi g-closed sets) and N s g-open sets (nano semi g-open sets) in nano topological spaces and certain properties are investigated. We also investigate and discussed their relationships with other forms of nano sets. Further, we have given an appropriate examples to understand the abstract concepts clearly.

The basic objective of this paper is to introduce and investigate the class of Nβ-regular spaces. The relationship among nano-regular space, nano semi-regular space, nano pre-regular space, nano α-regular space, nano T 0-space, nano T 1-space and nano T 2-space. Moreover, we define the forms of nano semi-p-regular, nano semi-p-p-regular and nano semi-p-s-regular spaces and study their properties.