I hope you are well.
I need your help:
Suppose X and Y are topological homeomorphic spaces such that X is a group. Then is it true that Y is also a group?
Two spaces are said to be homeomorphic if there is a bijective continuous function between them and the inverse of the function is also continuous.
Group is algebraic structure. a set X with binary operation * is a group if (1) * is associative that is x*(y*z)=(x*y)*z for all x,y,z in X. (2) there is an element e in X called the identity element which satisfy e*x=x*e=x, for all x in X. (3) for each element x in X there is an inverse x^-1 such that x*x^-1=x^-1*x=e.
Please help me and every guidance is highly appreciated.
Thank you in advance