Sobre conjuntos estratificados

• Ano de defesa: 1971
• Autor(a) principal: Teixeira, Marco Antonio
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: topologia diferencial
• Link de acesso: https://teses.usp.br/teses/disponiveis/18/0/tde-20250523-142258/

This paper is based upon the final part of the class-room notes compiled by prof. Lo.ibel on a course given by prof. R. Thom in 1961, in Berkeley, California. The subject covered by this course is incomplet and, in many places, vague unfortunately two articles by Prof. Thom [13] and [17] do not completely clerify several obscure points. It has been our partially archieved purpose to make these clear, to ilustrate several concepts with examples and aounter-examples and to complete spme proofs that were only sketched by Prof. Thom. Chapter 0 will give the main basic concepts used in the text; it is interesting to observe the definition of imbedding. Basic results on algebraic sets, semi-algebraic sets, carpeting function and Schubert Varieties will be rapidly displayed in Chapter 1. Some results that are mentioned and used, and that are not proved, have theis proof, if they are not trivial, l in the corresponding bibliography, which is named. Paragraph 4 has a corollary which will be explicitly demonstrated in Chapter 2. Chapter 2 has the definition of a Stratified Set, contains axions about this set and ends with an application of Transversality upon this set. This hypotheses, having the following been added the mapping is proper and F(Rn) intercepts each stratum on a finite number of conex components only. It is interesting to take note of the construction of example 2 -c. Chapter 3 presents the Stratified Mapping, the Fundamental System of Neighborhoods in a a Stratified Set, Degenerescency of a Stratified Mapping and two theorems ( # 3- 1 and 4 -1) that are very important. Special attention should be dedicated to examples 1-d and 3-b. Chaptef 4 has as its main purpose the construction of an example Prof. Thoms, which displays the need for the mapping to be without o- degenerescency, in theorem 4- 1 of Chapter 3. We shall also prove that a polynomial mapping, restricted to a semialgebraic set, is stratified. The proof of this fact follows the ideas discussed in example 1 - a of this chapter. The find pages countain thebibliography. At [13] some possible applications of this theory in (a) Topological Stability of Topological Mappings and (b) Triangularization of a differentiable mapping, are given.