On SC-Compact Spaces and Their Relations to Semi-Compact and s-Closed Spaces
Nasef, A., El-Bably, M., El-Gayar, M. (2025). On SC-Compact Spaces and Their Relations to Semi-Compact and s-Closed Spaces. EKB Journal Management System, 5(1), 29-37. doi: 10.21608/abas.2025.403342.1067
Arafa A. Nasef; Mostafa K. El-Bably; Mostafa A. El-Gayar. "On SC-Compact Spaces and Their Relations to Semi-Compact and s-Closed Spaces". EKB Journal Management System, 5, 1, 2025, 29-37. doi: 10.21608/abas.2025.403342.1067
Nasef, A., El-Bably, M., El-Gayar, M. (2025). 'On SC-Compact Spaces and Their Relations to Semi-Compact and s-Closed Spaces', EKB Journal Management System, 5(1), pp. 29-37. doi: 10.21608/abas.2025.403342.1067
Nasef, A., El-Bably, M., El-Gayar, M. On SC-Compact Spaces and Their Relations to Semi-Compact and s-Closed Spaces. EKB Journal Management System, 2025; 5(1): 29-37. doi: 10.21608/abas.2025.403342.1067

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

Advances in Basic and Applied Sciences
Volume 5, Issue 1, August 2025, Page 29-37  XML PDF (1.57 MB)
Document Type: Original Article
DOI: 10.21608/abas.2025.403342.1067
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Authors
Arafa A. Naseforcid 1; Mostafa K. El-Bablyorcid 2; Mostafa A. El-Gayar email orcid 3
1Department of Physics and Engineering Mathematics, Faculty of Engineering, Kafrelsheikh University, Kafrelsheikh, Egypt
2Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
3Department 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.
Keywords
C-compact; irresolute function; semi-compact space; s-closed space; quasi-H-closed space
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