O conceito de corte e a construção do contínuo
Lima Fortes, Paulino
Revista de Ciência e Tecnologia, Edições Uni-CV, Praia, 2013, págs. 69 - 84.ISSN 2307-4019, (2013), 8, 69
The idea of “cut” seems to be one of the primary geometric intuitions of the human mind, by the testimony that constitute the various discoveries, rediscoveries and generalizations of that concept, as well as the resource that it makes whenever it is needed an abstract definition of the geometric idea of continuity. Since its first known approach by Eudoxus of Cnid, passing by Euclid of Alexandria, the revolutionary formulation of Dedekind, after passing by the non-Archimedean generalization
of Veronese, formulations Schöenflies, Otto Hölder, Felix Hausdorff and John Conway, among others (before and after),
the concept of cut camp sat on all fronts of development of mathematical ordered systems. In this article we will
be making a brief visit to the concept of cut, following its historical evolution, together with the characterization of the resulting continuum.