Funciones de una variable real con valores en un espacio vectorial de convergencia. I. Derivadas.
Any order derivations of functions of a real variable with values in a convergence vector space over R (c.v.s.) have been defined. This will allow us to develop (in a following paper) the integration for this type of functions. Some results have been obtained: we build up a c.v.s. isomorphism between a c.v.s. F and the c.v.s. L(R;F) -the continuous linear mappings of R into F endowed with the continuous convergence structure A-. We prove a function f: R → F to be of class C if, and only if, it is...