On Retractions of Lobachevsky Space

Abstract

Our aim in the present article is to introduce and study new types of retractions of Lobachevsky space. Types of the deformation retracts of Lobachevsky space are presented. The relations between the folding and the deformation retract of Lobachevsky space are deduced. Types of minimal retractions of Lobachevsky space are also presented. Also, the isometric and topological folding in each case and the relation between the deformation retracts after and before folding have been obtained. New types of homotopy maps are deduced. Theorems governing this connection are achieved.

Our aim in the present article is to introduce and study new types of retractions of Lobachevsky space. Types of the deformation retracts of Lobachevsky space are presented. The relations between the folding and the deformation retract of Lobachevsky space are deduced. Types of minimal retractions of Lobachevsky space are also presented. Also, the isometric and topological folding in each case and the relation between the deformation retracts after and before folding have been obtained. New types of homotopy maps are deduced. Theorems governing this connection are achieved.

Cite this paper

A. El-Ahmady and K. Al-Onemi, "On Retractions of Lobachevsky Space,"*Applied Mathematics*, Vol. 4 No. 3, 2013, pp. 491-498. doi: 10.4236/am.2013.43073.

A. El-Ahmady and K. Al-Onemi, "On Retractions of Lobachevsky Space,"

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