Foldings and Deformation Retractions of Hypercylinder

A  E  El Ahmady; N Al Hazmi

doi:10.17485/ijst/2013/v6i2.23

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Foldings and Deformation Retractions of Hypercylinder

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2013/v6i2.23

Year: 2013, Volume: 6, Issue: 2, Pages: 1-10

Original Article

Foldings and Deformation Retractions of Hypercylinder

^1,2 A. E. El-Ahmady, ² N.Al-Hazmi

²Mathematics Department, Faculty of Science,
¹ Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt. [email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Our aim in the present work is to introduce and study new types of retractions of hypercylinder. Types of the deformation retracts of hypercylinder are presented. The relations between the folding and the deformation retract of hypercylinder are deduced.Types of minimal retractions of hypercylinder are introduced. Also, the isometric and topological folding in each case and the relation between the deformation retracts after and before folding are obtained. New types of homotopy maps are deduced. Theorems governing this connection are achieved.
Keywords: Hypercylinder, Retraction, Folding.