Strong GP-continuity and weakly GP-closed functions on GPT spaces

Abstract

In this research article, we present the procedure of generating GPT spaces in two different ways: using the generalized neighbourhood system and the monotonic operator. Then, we introduce several types of generalized primal continuous functions. Some characteristics have been dissected, and the relationships among them have been studied. We use the technique of Császár, which changes the “generalized topology” to other “generalized topologies” weaker than it, to show some important results. Furthermore, we show that the notion of “strong GP-continuity” coincides with the notion “GP-continuity” under some conditions. We present these results on a simple graph to make it easier for the reader. Finally, study the preservation of the notions of “GP-connected” and “GP-hyperconnected” by different types of generalized primal continuous functions.

Keywords

• GP-continuous
• GPN-continuous
• Strong GP-continuous
• Weakly GP-closed
• GP-connected
• GP-hyperconnected