On α–Lindelöf in Bitopological Space
DOI:
https://doi.org/10.19139/soic-2310-5070-4008Keywords:
α-open set, α-Lindelöf space, α-compact space, bitopological space, pairwise coverAbstract
This paper studies α-Lindelöf covering properties in bitopological spaces by means of the associated α-topologies. For a bitopological space (E, ξ1, ξ2), the central method is the identification of α-open subsets of (E, ξi) with ordinary open subsets of (E, ξα i ). This allows α-Lindelöfness and related covering properties to be treated through classical Lindelöf theory. We establish the equivalence between α-Lindelöfness of (E, ξi) and Lindelöfness of (E, ξαi ), formulate componentwise and pairwise-cover versions in bitopological spaces, and introduce corresponding α-Lindelöf numbers. Cardinal bounds in terms of network weight and weight are obtained, and a countable-sum formula for the α-Lindelöf number is proved. We also analyze the relation between α-Lindelöfness, α-compactness, and α-countable compactness, supported by examples separating the principal notions. Finally, preservation under strongly α-continuous mapsDownloads
Published
2026-09-17
How to Cite
Atoom, A. A., Malkawi, A. A.-R., Bani Abdelrahman, M., & Rabaiah, A. (2026). On α–Lindelöf in Bitopological Space. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-4008
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Copyright (c) 2026 Ali A. Atoom, Abed Al-Rahman M. Malkawi, Mohammad Bani Abdelrahman, Ayat M. Rabaiah
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