On Algebraic and Topological Properties of Some Fundamental Groups
Laurent Djerassem1, Daniel Tieudjo2
1Djerassem Laurent, Department of Mathématiques, Université de Ndjamena Tchad, Faculté des Sciences Exactes et Appliquées Ndjamena Tchad, Ndjamena, Commune de Ndjamena, Chad.
2Prof. Daniel Tieudjo, Associate Professor, Department of Mathématiques, Université de Ngaoundere, Ngaoundere Cameroon.
Manuscript received on 28 September 2024 | First Revised Manuscript received on 03 November 2024 | Second Revised Manuscript received on 16 February 2025 | Manuscript Accepted on 15 April 2025 | Manuscript published on 30 April 2025 | PP: 5-10 | Volume-5 Issue-1, April 2025 | Retrieval Number: 100.1/ijam.B117704021024 | DOI: 10.54105/ijam.B1177.05010425
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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: In this paper, we study the algebraic and topological properties of some topological spaces. We note that the fundamental group of a topological group is abelian and we study some spaces of the same homotopy type with the unit circle S1 . The basic group of the unit circle S1 is isomorphic to the additive group of integers. We say that a topological space is simply connected if it is path-connected and has a trivial fundamental group. We show that the fundamental group of a n-punctured plane is free and we characterize some surfaces as topologically distinct.
Keywords: Homeomorphism, Path, Loop, Topological Group, Fundamental Group, Free Product.
Scope of the Article: Topology