TITLE: 
                        
                            The Homotopical Proof of  Π1 (S, xo) as a Fundamental Group in a General Interval
                                
                                
                                    AUTHORS: 
                                            Zigli David Delali, Obeng-Denteh William, Brew Lewis, Ansah Richard Kwame 
                                                    
                                                        KEYWORDS: 
                        Homotopy, Fundamental Group, Homeomorphism, Equivalent Class, Path Concatenation 
                                                    
                                                    
                                                        JOURNAL NAME: 
                        Advances in Pure Mathematics,  
                        Vol.11 No.5, 
                        May
                                                        17,
                        2021
                                                    
                                                    
                                                        ABSTRACT: The aim of this study is to establish that, the equivalent class  which is made up of homotopic loops is a group with respect to  in the general interval [m,n]. The study proved from homotopical point of view that  is associative, has an identity and inverse function. The study established with proof thatis a fundamental group in [m,n] ,.