A Note on the Theory of Topological Spaces and Topological Variety

In this paper, we study some concepts of algebraic topology. The basic idea is to transform a topological problem into an algebraic problem. The method consists of describing the topological structure of a space, associating with it an algebraic object. At each topological space X we associate a ring or an R-module and to the continuous functions we associate a homomorphism of rings or an R homomorphism, where R is a commutative ring with identity not null.