David Delali Zigli, William Obeng-Denteh and Isaac Owusu-Mensah, On the Candid Appraisal of the Proof of $\prod_{1}(S,x_{o})$ as a Fundamental Group with respect to "$\circ$", Volume 2017, Number 6, Pages 20-26, 2017

# David Delali Zigli, William Obeng-Denteh and Isaac Owusu-Mensah, On the Candid Appraisal of the Proof of $\prod_{1}(S,x_{o})$ as a Fundamental Group with respect to "$\circ$", Volume 2017, Number 6, Pages 20-26, 2017

Abstract: It is known that a homeomorphism between two topological spaces preserves all the topological properties such as connectedness and compactness. To a map of spaces we can associate a homomorphism of groups such that compositions of maps yield compositions of homomorphisms of groups. Then any thing we can say about a topological situation gives information about the algebraic one. In this paper we studied and proved with self explained diagrams that $\prod_1(S,x_0)$ is a fundamental group with respect to "$\circ$" from the homotopical point of view. We made it more comprehensible, self explanatory and user friendly with clear diagrams. This is of interest because it can be used as a great tool in mathematics to prove many facts.

Keywords: Homotopy, Fundamental group, Homomorphism, Homeomorphism, Juxtaposition.

David Delali Zigli, William Obeng-Denteh and Isaac Owusu-Mensah, On the Candid Appraisal of the Proof of $\prod_{1}(S,x_{o})$ as a Fundamental Group with respect to "$\circ$", International Journal of Advances in Mathematics, Volume 2017, Number 6, Pages 20-26, 2017.