New Type of Strongly Continuous Functions in Topological Spaces via δ-β-Open Sets

Alaa Mahmood Farhan, Xiao Song Yang

Abstract

In this paper we introduce and investigate a new class of strong continuous functions called strongly θ-δ-β-continuous functions by using two new strong forms of δ-β-open sets called δ-β-regular sets and δ-βθ-open sets. This class is a generalization of both strongly θ-e-continuous functions and strongly θ-β-continuous functions. Severalnew characterizations and fundamental properties concerning strongly θ-δ-β-continuous functions are obtained. Furthermore, the relationships between strongly θ-δ-β-continuous functions and other well-known types of strong continuity are also discussed.   

 

Keywords

δ-β-open sets, δ-βθ-closed sets, δ-β-regular sets, strongly θ-δ-β-continuity.

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