MODEL OF LINEAR FUNCTIONAL, CERTAIN ON THE TOPOLOGY OF IMAGE

Abstract

There is developed the presentation of the vector function of that determined on the fragmentary topologies of images. On the basis of this presentation the model of functional from the space of open covering into the space of real number is proposed. Well-proven linearness of this functional enables to enter the operation of addition and multiplying by scalars for operators, certain on separabel gil'bertovykh spaces, and for tasks, related to factorization of these spaces. It is set that the linearness of offered functional is given by possibility to pass to the construction and analysis of additive groups of functional reflections, certain on the discrete topology of image.