Infra Pre-open Sets and Their Applications to Generate New Types of Operators and Maps

Abstract

Herein, we introduce the concepts of infra soft pre-open infra soft pre-closed sets which are respectively generalizations of infra soft open and infra soft closed sets.
We characterize them and investigate their behaviours under infra soft homeomorphism maps and finite product of soft spaces. Then, we apply infra soft pre-open infra soft pre-closed sets to define the operators of infra pre-interior, infra pre-closure, infra pre-limit and infra pre-boundary. We discuss their main properties and show the interrelations between them. In the end, we introduce new types of soft maps using infra soft pre-open and infra soft pre-closed sets and explore their essential properties.