Existence and construction of the Peano selection for a multivalued function

In the present article, the necessary conditions are presented for a multivalued function in order to define a Peano selection. To achieve this, a bibliographic review was carried out on general results of compact topological spaces, open and closed sets and continuity. To then address the same topics, but on metric spaces. Next, the theory of multivalued functions was studied, specifically semicontinuity, both superiorly and inferiorly. Finally, using the General Theorem of multivalued functions, the necessary conditions are determined for the multivalued function, F : [0, 1]-->[0, 1] × [0, 1] to admit the construction of the selection of Peano.