On SC-Compact Spaces and Their Relations to Semi-Compact and s-Closed Spaces

Document Type : Original Article

Authors

1 Department of Physics and Engineering Mathematics, Faculty of Engineering, Kafrelsheikh University, Kafrelsheikh, Egypt

2 Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

3 Department of Mathematics, Faculty of Science, Helwan University, Helwan, Egypt

Abstract

This study proposes and examines a novel category of topological spaces, termed SC-compact spaces. Positioned between the classical notions of semi-compactness and C-compactness, the SC-compact class is shown to possess the s-closed property as defined by Di Maio and Noiri. Using the framework of semi-open and semi-closed sets, the paper investigates the defining characteristics of SC-compactness and situates it within the broader landscape of generalized compactness concepts. The analysis further explores the behavior of SC-compact spaces under various mappings—such as semi-continuous and irresolute functions—revealing fundamental relationships with established topological structures. Several examples illustrate these theoretical connections and emphasize the distinctive role of SC-compactness among other compactness conditions. The findings contribute to the theoretical development of compactness in topology and suggest promising directions for further extensions and applications, particularly in contexts where semi-open coverings and neighborhood systems are central. Overall, this work deepens the foundational understanding of topological compactness and opens new perspectives for research in fields involving approximation and structural imprecision.

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