On the Relation Between Topological Free and Topological Dual Injective Modules

Algebraic topology is a branch of mathematics which use the concepts of abstract algebra to study topological spaces in which to find algebraic invariants that classify topological spaces up to homeomorphism. In this paper, the basic properties of some concepts on algebraic topology such as the topological ring, the topological module, and the topological free module were recalled, which were helped to define new concepts and proof some of there properties as a new results. Then, some results related to the relation between the free topological module and homomorphism topology. As in any application will be introduced, the tensor concept will be chosen to explain the new results related to the topological module.