Topological Modules/Constructions

quotient topological module Let be a topological module over the topological ring , and let a submodule with the subspace topology. Then the module together with the quotient topology, ie. the final topology induced by the quotient map , is called the quotient module of . quotient map of topological quotient is open Let be a topological module and a submodule. Then the map is open. Let be any open set. We have which is open as the union of open sets. quotient topological module is topological module Let be a topological module and a submodule. Then the quotient module is a topological module with the subspace topology.