Tri-Expandability and Product Spaces in Tri-Topological Spaces

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-23-2025-192
Published: Aug 15, 2025
Cite as:
Jamal Oudetallah, Rehab Alharbi, Salsabiela Rawashdeh, Ala Amourah, Tala Sasa, Tri-Expandability and Product Spaces in Tri-Topological Spaces, Int. J. Anal. Appl., 23 (2025), 192.

Main Article Content

Jamal Oudetallah, Rehab Alharbi, Salsabiela Rawashdeh, Ala Amourah, Tala Sasa

Abstract

In this paper, we introduce and investigate the notion of tri-expandability in tri-topological spaces as a natural generalization of expandability in classical topological spaces. We establish fundamental characterizations of tri-expandable spaces and explore their behavior under product operations. The main results include a comprehensive study of the relationships between various forms of tri-expandability and their connections to classical expandability properties. We prove that tri-expandability is preserved under certain product constructions and provide necessary and sufficient conditions for a tri-topological space to be tri-expandable. Our findings extend the classical theory of expandable spaces to the multi-topological setting and reveal new structural properties that are unique to the tri-topological framework. Several illustrative examples demonstrate the richness of the theory and highlight the differences from the classical case.

Article Details

References

  1. L.L. Krajewski, On Expanding Locally Finite Collections, Can. J. Math. 23 (1971), 58–68. https://doi.org/10.4153/cjm-1971-006-3.
  2. J.C. Smith, L.L. Krajewski, Expandability and Collectionwise Normality, Trans. Am. Math. Soc. 160 (1971), 437–451. https://doi.org/10.2307/1995819.
  3. H.W. Martin, Product Maps and Countable Paracompactness, Can. J. Math. 24 (1972), 1187–1190. https://doi.org/10.4153/cjm-1972-128-7.
  4. Y. Katuta, Expandability and Product Spaces, Proc. Jpn. Acad. Ser. Math. Sci. 49 (1973), 449–451. https://doi.org/10.3792/pja/1195519303.
  5. J. Oudetallah, Nearly Metacompact in Bitopological Space, Int. J. Open Probl. Comput. Math. 15 (2022), 6–11.
  6. J. Oudetallah, M. AL-Hawari, Other Generalization of Pairwise Expandable Spaces, Int. Math. Forum 16 (2021), 1–9. https://doi.org/10.12988/imf.2021.912116.
  7. J. Oudetallah, M.M. Rousan, I.M. Batiha, On D-Metacompactness in Topological Spaces, J. Appl. Math. Inf. 39 (2021), 919–926. https://doi.org/10.14317/JAMI.2021.919.
  8. J. Oudetallah, R. Alharbi, I.M. Batiha, On r-Compactness in Topological and Bitopological Spaces, Axioms 12 (2023), 210. https://doi.org/10.3390/axioms12020210.
  9. J. Oudetallah, L. Abualigah, h-Convexity in Metric Linear Spaces, Int. J. Sci. Appl. Inf. Technol. 8 (2019), 54–58.
  10. J. Oudetallah, Novel Results on Nigh Lindelöfness in Topological Spaces, Int. J. Anal. Appl. 22 (2024), 153. https://doi.org/10.28924/2291-8639-22-2024-153.