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On Cℵ-fibrations in bitopological semigroups.
Suliman Dawood1, Adem Kılıçman2
1Department of Mathematical Sciences, Hodeidah University, Hodeidah, Yemen.
Thescientificworldjournal
|September 13, 2014
Summary
This study extends the path lifting property to bitopological semigroups, revealing its significance for C(ℵ)-fibrations and their connection to approximate fibrations.
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.
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