On 𝑷𝜷-Open Sets and 𝑷𝜷-Irresolute Functions

Abstract

The main purpose of this paper is to introduce and study generalization of open sets called 𝑃𝛽- open. This class is weaker than the class 𝑝𝜃-open sets and stronger than the class pre-open sets. We studied the relation between these sets with other types of open sets and we gave several characterization about these sets. Also, we defined and investigated class of functions called 𝑃𝛽-irresolute and 𝑃𝛽 ∗ - Irresolute. Several properties and interesting haracterization concerning of these a new types of functions are obtained.