Al-Refaei, Abdulkafi; Dawood, Suliman On extending \(S \aleph\)-fibrations to \(C \aleph\)-fibrations in bitopological semigroups. (English) Zbl 1470.54018 Int. J. Adv. Appl. Math. Mech. 7, No. 3, 77-84 (2020). Summary: In this paper, we start by giving the concepts of bitopological semigroups and study some their properties. Then we extend the concepts of \(S \aleph\)-fibrations in the homotopy theory for topological semigroups to bitopological semigroups by giving the concept of \(C \aleph\)-fibrations. Furthermore, we study some properties on \(C \aleph\)-fibrations such as a restriction property, composition property, a product property, and a covering homotopy theorem. MSC: 54E55 Bitopologies 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) 22A15 Structure of topological semigroups 55R05 Fiber spaces in algebraic topology Keywords:bitopological space; fibration; homotopy relation × Cite Format Result Cite Review PDF Full Text: Link References: [1] D. Coram and f. Duvall, Approximate fibrations, Rocky Mountain J. Math. 7 (1977), 275-288. · Zbl 0367.55019 [2] D. Coram and f. Duvall, Approximate fibrations and amovability condition for S-maps, Pacific J. Math. 72 (1977), 41-56. · Zbl 0368.55016 [3] E.H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966. · Zbl 0145.43303 [4] M. Lawson, J. Matthews, T. Porter, The homotopy theory of inverse semigroups, International Journal of Algebra and Computation 12 (2002) 755-790. · Zbl 1050.55004 [5] R. C. Kirby, L. C. Siebenmann, Foundational Essays On Topological Manifolds, Smoothings, And Triangulations. Annals of Math. Studies 88, Princeton University Press, Princeton, NJ, 1977. · Zbl 0361.57004 [6] W. Hurewicz, On the concept of fiber space, Proc. Nat. Acad. Sci. USA 41(1955), 956-961. · Zbl 0067.15902 [7] J.C. Kelly, Bitopological spaces, Proc. London Math. Soc. (3) 13 (1963) 71-89. · Zbl 0107.16401 [8] J.L. Kelley, General Topology, Springer, New York, 1955. IntroductionPreliminariesBitopological semigroups C-fibrationsCovering homotopy propertyReferences This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.