Specific types of Lindelöfness and compactness based on novel supra soft operator

Alaa M. Abd El-latif; Alaa M. Abd El-latif

doi:10.3934/math.2025374

AIMS Mathematics

2025, Volume 10, Issue 4: 8144-8164. doi: 10.3934/math.2025374

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Specific types of Lindelöfness and compactness based on novel supra soft operator

Alaa M. Abd El-latif ^,

Mathematics Department, College of Science, Northern Border University, Arar 91431, Saudi Arabia

Received: 20 February 2025 Revised: 18 March 2025 Accepted: 28 March 2025 Published: 09 April 2025
MSC : 03E72, 54A05, 54B10, 54C10

The aim of this study was to originate six types of generalized compactness and Lindelöfness in the frame of supra soft topological spaces (or SSTSs) based on the approaches of supra soft somewhere dense sets (or SS-sd-sets) and the SS-sd-closure operator, named SS-sd-almost compact (Lindelöf) spaces, SS-sd-approximately compact (Lindelöf) spaces and SS-sd-mildly compact (Lindelöf) spaces. The essential properties of each type of the aforementioned notions were studied. Specifically, we studied the invariance of these notions under specific types of soft mappings. Moreover, the relationships among these notions and between corresponding notions were discussed. Furthermore, the equivalence among them was proved under the SS-sd-partition condition. Finally, we provided a diagram to summarize these relationships with the support of concrete counterexamples.
- supra soft sd-closure operator,
- SS-sd-almost compactness,
- SS-sd-hyperconnectedness,
- SS-sd-approximately Lindelöfness,
- SS-sd-mildly compactness,
- SS-sd-partition
Citation: Alaa M. Abd El-latif. Specific types of Lindelöfness and compactness based on novel supra soft operator[J]. AIMS Mathematics, 2025, 10(4): 8144-8164. doi: 10.3934/math.2025374

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Abstract

The aim of this study was to originate six types of generalized compactness and Lindelöfness in the frame of supra soft topological spaces (or SSTSs) based on the approaches of supra soft somewhere dense sets (or SS-sd-sets) and the SS-sd-closure operator, named SS-sd-almost compact (Lindelöf) spaces, SS-sd-approximately compact (Lindelöf) spaces and SS-sd-mildly compact (Lindelöf) spaces. The essential properties of each type of the aforementioned notions were studied. Specifically, we studied the invariance of these notions under specific types of soft mappings. Moreover, the relationships among these notions and between corresponding notions were discussed. Furthermore, the equivalence among them was proved under the SS-sd-partition condition. Finally, we provided a diagram to summarize these relationships with the support of concrete counterexamples.

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