Normal subobjects of topological groups and of topological semi-Abelian algebras

As any category Gp(E) of internal groups in a given category E, the category Gp(Top) of topological groups possesses the strong algebraic property of protomodularity which carries intrinsic notions of normal subobject and of centrality. Here we explicit and investigate these intrinsic notions in the category Gp(Top). We extend these results to any category TopT of topological semi-Abelian algebras.