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On Cℵ-fibrations in bitopological semigroups.

Suliman Dawood1, Adem Kılıçman2

  • 1Department of Mathematical Sciences, Hodeidah University, Hodeidah, Yemen.

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This study extends the path lifting property to bitopological semigroups, revealing its significance for C(ℵ)-fibrations and their connection to approximate fibrations.

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Area of Science:

  • Topology
  • Algebraic Topology
  • Semigroup Theory

Background:

  • Homotopy theory investigates continuous deformations of maps.
  • Topological spaces and their properties are fundamental in mathematics.
  • Bitopological semigroups combine topological and algebraic structures.

Purpose of the Study:

  • To extend the path lifting property from topological spaces to bitopological semigroups.
  • To elucidate the role of this extended property in C(ℵ)-fibrations.
  • To establish the relationship between C(ℵ)-fibrations and approximate fibrations.

Main Methods:

  • Generalization of the path lifting property.
  • Homotopical analysis within the framework of bitopological semigroups.
  • Investigation of C(ℵ)-fibration properties and approximate fibrations.

Main Results:

  • Successful extension of the path lifting property to bitopological semigroups.
  • Demonstration of the path lifting property's crucial role in C(ℵ)-fibrations.
  • Proof of the relationship between C(ℵ)-fibrations and approximate fibrations.

Conclusions:

  • The path lifting property is a key concept transferable to more complex algebraic-topological structures.
  • C(ℵ)-fibrations exhibit a strong connection to approximate fibrations, unified by the path lifting property.
  • This research deepens the understanding of fibration properties in generalized topological settings.