Homotopias definidas por continuidade generalizada

Abstract

This monograph was the result of a scientific initiation research carried out within the scope of the Tutorial Education Program, which aimed to propose new notions of homotopies based on the concept of generalized continuity introduced by Vieira in [4]. The study of generalized continuity of functions, in turn, is an evolution of the ideas of generalized limits of functions introduced by Vieira and Braz in [1]. This monograph is constituted as an academic text with the following purposes: to be a complementary bibliographic option for some basic mathematical contents related to the area of ​​Topology; to be a bibliographic option in Portuguese for the dissemination of some specialized scientific results on generalized continuity; and to contribute with original results on homotopies and functions with generalized continuity obtained by the author of the monograph in partnership with the mathematicians Vieira and Braz mentioned above. The title of the work is called Homotopias defined by generalized continuity, since the concepts introduced here are linked to functions that have continuity in the generalized sense. In addition, the work brings some additional considerations and some original results regarding generalized continuity, aiming to assist in the development of the technical framework necessary for the understanding and consistency of the proposed notions of generalized homotopies.