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| Quasi-Pre-Semi-Open Sets: A Weaker Notion in Topology
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Ahmed M. Rajab , Falah Mahdi Atshan , Ohood A. Hadi
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Abstract:
The concept of quasi-presemi-open sets (Qpsos) is a generalization of presemi-open sets, which themselves are a generalization of semi-open sets. Qpsos. provide a more flexible notion of openness in topological spaces, allowing for finer distinctions between open and closed sets.This paper, we explore the properties and characteristics of Qpsos. We define the notion of qps-open sets in terms of their complement, which exhibits some similarities to the definition of presemi-open sets. We investigate the relationships between Qpsos and other types of sets, such as open sets, closed sets, and presemi-open sets. Furthermore, we examine the behavior of Qpsos under various operations, including union, intersection, and closure. We establish necessary and sufficient conditions for a set to be qps-open, and we discuss the implications of these conditions on the topology of a space.We also investigate the role of Qpsos in the context of continuity and compactness. We explore the connection between qps-continuous functions and other types of continuous functions, and we analyze the relationship between Qps -compactness and other notions of compactness.
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