Epsilon teoria de pontos fixos e coincidências

Abstract

This dissertation is a study of the so-called epsilon theories of fixed points and coincidences, developed since 2006. With the same research proposals as the Nielsen theory for fixed points and coincidences, epsilon theories originate with the imposition of a restriction to the type of deformation by homotopy to which functions may be subjected. The restriction consists of considering a positive real number ε given a priori and then allow only deformations by ε-homotopies, that is, homotopies whose deformation at each point is less than ε. In a specific scenario that allows this type of approach, the so-called ε-minimum numbers of fixed points and coincidences and ε-Nielsen numbers for fixed points and coincidences – lower limits for the first – are defined, and the Wecken property is discussed in this context.