If X is a path connected topological group whose underlying topology has a simply connected cover and p:X, e → X, e is a covering map of topological spaces then X, x_0 becomes a topological group with identity e and p is a morphism of topological groups. In this paper we prove a similar result for H-spaces result rather than topological groups. Further we give a result on the lifting of the local morphisms of H-spaces to a cover.
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