Un estudio sobre los espacios vectoriales topológicos

Abstract

In the study of the normed, metric and topological spaces, interesting characterizations and properties emerge about them. Examples of these are the continuity of functions, invariants, transformations between spaces, ideas of distance, among others. What we want to do here is try to start from the vector spaces and weaken their properties, giving it only a topology that meets certain characteristics. Vector spaces with F-norm-induced topologies appear, remaining between these spaces. These induce a topology compatible with the operations of the vector space, just as other generalizations maintain classical properties. Our job now is to verify what properties we can keep in this space.