One can check that there exists a TopGrStr which is strict and non empty. One can verify that there exists a non empty TopGrStr which is strict, topological space-like, and trivial. Let G be a group-like associative non empty TopGrStr. Then -1 G is a map from G into G . Let G be a group-like associative non empty TopGrStr.
G is continuous.
Let G be a topological space-like TopGrStr. A TopologicalGroup is a UnContinuous BinContinuous TopGroup. Let T be a BinContinuous non empty topological space-like TopGrStr, a , b be elements of the carrier of T , and W be a neighbourhood of a b . Let T be a topological space-like non empty TopGrStr. Then T is BinContinuous.