International Journal of Advances in Mathematics
International Journal of Advances in Mathematics
2456-6098
Volume 2017
Number 6
2017
November
01
On the Candid Appraisal of the Proof of $ \prod_{1}(S,x_{o}) $ as a Fundamental Group
with respect to $ \circ $
20
26
EN
William
Obeng
Denteh
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Ghana.
Zigli
David Delali
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Ghana.
davidzigli@gmail.com
Isaac
Owusu Mensah
Department of Science Education, University of Education Winneba, Mampong-Ashanti, Ghana.
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 \textquotedblleft $ \circ $\textquotedblright 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.
Homotopy, Fundamental group, Homomorphism, Homeomorphism, Juxtaposition.
http://adv-math.com/2017/11/01/william-obeng-denteh-zigli-david-delali-isaac-owusu-mensah2on-candid-appraisal-proof-prod_1sx_o-fundamental-group-respect-circ-volume-2017/
http://adv-math.com/wp-content/uploads/2017/10/FINAL-ADV-201738.pdf