Mixed Structure of Approximate Serre Cofibration
Keywords:
CW- Complex, Lowering Homotopy Property, Mixed Approximate Serre Cofibration, Homotopy Extension Property, M- CriterionAbstract
This paper introduces a novel concept called Mixed Approximate Serre Cofibration (MASCof), aimed at extending the structure of the traditional Serre cofibration. The main objective of this research is to define the mixed structure and prove that the majority of theorems valid for Serre cofibrations also apply to mixed approximate Serre cofibrations. Using a qualitative mathematical approach, the study demonstrates properties of MASCof and its application within CW-complex spaces. Several key theorems and propositions are presented, proving that products, pullbacks, and closed subspaces of mixed approximate Serre cofibrations retain their structural properties. The results provide insights into the homotopy extension property and mixed neighborhood deformation retracts, broadening the understanding of topological constructs.
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A.Strom, “Note on Cofibrations”, Math, scand.19 (1966).
Armin Rainer,Wien, “ Orbit Projections as Fibrations”, Czechoslovak Mathematical Journal,V 59, No 134, p 592-538, 2009
Ch. Lin, “Introductory Differential Topology And An Application To The Hopf Fibration”, University of Chicago, June,2020.
D. W. Al Baydli, A. A.Hussien “Mixed Cofibration and Mixed Hurewicz Cofibration ” ,University of Anbar-Education college of woman, Wassit University-College of Science,2009.
H.J, Mustafa, “Some theorems on Fibration and Cofibration”, Ph.Dr.Thesis ,Califor- nia University ,Los Angeles ,1972.
J.P, May, “A Concise Course in Algebraic Topology”, University of Chicago press, 1st edition (September 1, 1999).
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Published
2024-10-08
How to Cite
Noor, A. J. ., & Baydli, D. . W. A. . (2024). Mixed Structure of Approximate Serre Cofibration. CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 5(4), 359–367. Retrieved from https://cajmtcs.casjournal.org/index.php/CAJMTCS/article/view/668
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