Mathematics and Statistics Vol. 11(3), pp. 607 - 615
DOI: 10.13189/ms.2023.110319
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Product Properties for Generalized Pairwise Lindelöf Spaces

Zabidin Salleh ^1,*, Muzafar Nurillaev ², Che Mohd Imran Che Taib ^1
1 Department of Mathematics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Malaysia
² Tashkent State Pedagogical University Named after Nizami, 100070 Tashkent, St. Bunyodkor, 27, Uzbekistan

ABSTRACT

In topological spaces, although compactness is satisfying the product invariant properties, but for the Lindelöffness, it is not preserved by the product unless one or more factors are assumed to satisfy additional conditions. Similar results yield for the bitopological spaces, that is, the property of pairwise Lindelöf bitopological spaces is not preserved under the product unless one or more factors are assumed to be satisfy additional conditions, for instance, -spaces. The Cartesian product for arbitrarily many bitopological spaces was defined by Datta in 1972. Since then, many researchers have begun their study for the product bitopological spaces for their reason and direction. In this paper, we shall study finite product of pairwise nearly Lindelöf, pairwise almost Lindelöf and pairwise weakly Lindelöf spaces. We show that, all these generalized pairwise Lindelöf spaces are not preserved under a product by some counterexamples provided. Furthermore, we give some necessary conditions for these three bitopological spaces to be preserved under a finite product. Such condition is that one or more of the spaces has to be -space or the product have to be pairwise weak -space. Another interesting result is that the projection of these generalized pairwise Lindelöf spaces product with -space is a closed map.

KEYWORDS
Bitopological Space, -Nearly Lindelöf, -Almost Lindelöf, -Weakly Lindelöf, Product Bitopology

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Zabidin Salleh , Muzafar Nurillaev , Che Mohd Imran Che Taib , "Product Properties for Generalized Pairwise Lindelöf Spaces," Mathematics and Statistics, Vol. 11, No. 3, pp. 607 - 615, 2023. DOI: 10.13189/ms.2023.110319.

(b). APA Format:
Zabidin Salleh , Muzafar Nurillaev , Che Mohd Imran Che Taib (2023). Product Properties for Generalized Pairwise Lindelöf Spaces. Mathematics and Statistics, 11(3), 607 - 615. DOI: 10.13189/ms.2023.110319.