On extending \(S \aleph\)-fibrations to \(C \aleph\)-fibrations in bitopological semigroups. (English) Zbl 1470.54018

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.


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
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