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September 10, 2025Open Access

G-Compact Spaces Characterized by the Intersection of Countable Neighborhoods

Key Points

The research reveals connections among g-compactness, g-lindelöfness, and compactness, enhancing understanding in topology.
Key theorems illustrate how g-countably compactness relates to traditional compact and lindelöf spaces within topological frameworks.
Definitions of g-separation axioms are introduced using gδ sets, expanding the theoretical landscape in topology.
Examples provided clarify the intricate relationships between these concepts, contributing to the field's foundational knowledge.

Abstract

In this research, we introduce and analyze the concepts of \ (G\) -compactness, \ (G\) -Lindelofness, and \ (G\) -countably compactness within the framework of topological spaces, which are characterized by more rigorous conditions compared to those governing compact and Lindelof spaces. We formulate a series of theorems and present a variety of examples to clarify the relationships among \ (G\) -compactness, \ (G\) -Lindelofness, compactness, and Lindelofness. Additionally, we define the \ (G\) -separation axioms utilizing G_ sets and explore the interrelations among these concepts.

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