The uniqueness of binary operation on semilocally simply connected, connected and locally path connected topological groups

Given a topological group X with unity e. Suppose that X satisfies semilocally simply connected, locally path connected and connected condition. For every connected covering space ($\tilde{X}$, q) of X, there is a binary operation such that $\tilde{X}$ becomes a topological group with unity r, q(r) = e and q becomes a group homomorphism. In this paper, we show that there is a unique binary operation on $\tilde{X}$ such that it is a topological group with unity r and q is a group homomorphism. (paper)