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Universidade Estadual de Campinas

1.
Calefe, Michele, 1981-.
Construção *de* conjuntos numéricos : dos números inteiros aos hiperreais: Construction of the numerical sets : from integer to hyperreal numbers.

Degree: 2016, Universidade Estadual de Campinas

URL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/321576

Abstract: The goal of this work is to make the construction of the numerical sets of the integer, rational, real and hyperreal numbers. For the construction of the integer and rational numbers it was used the book "Números reais" by Jorge Aragona. In the case of the real numbers it was used the book "Principles of Mathematical Analysis" by Walter Rudin and for the construction of the hyperreal numbers it was used the text "An introduction to the Non-Standard Analysis" by Isaac Davis. These texts were used to guide this work, which also includes details not made by these authors. The construction of numerical sets, in general, shows very similar characteristics. From a set, which serves as a base to define an element that will be identified as elements in a new set, which will be created through isomorphism. The constructions of integer, rational and hyperreal numbers made here use equivalence classes, which does not happen in the construction of the real numbers that were made using the Dedekind cuts, in this dissertation. In addition to Dedekind cuts, there are other ways to construct real numbers. Cantor, for instance, made the construction of real numbers using Cauchy sequences, which are going to be commented briefly here. Besides the construction mentioned above, the last chapter gives suggestions about how to introduce studied topics in the high school mathematics level, exemplifying activities and passages about mathematics history that can be used
*Advisors/Committee Members: UNIVERSIDADE ESTADUAL DE CAMPINAS (CRUESP), Catuogno, Pedro Jose, 1959- (advisor), Universidade Estadual de Campinas. Instituto de Matemática, Estatística e Computação Científica (institution), Programa de Pós-Graduação em Matemática em Rede Nacional (nameofprogram), Andreani, Roberto (committee member), Barros, Tomas Edson (committee member).*

Subjects/Keywords: Números reais; Números hiperreais; Dedekind, Cortes de; Real numbers; Hyperreal numbers; Dedekind cuts

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Calefe, Michele, 1. (2016). Construção de conjuntos numéricos : dos números inteiros aos hiperreais: Construction of the numerical sets : from integer to hyperreal numbers. (Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/321576

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Calefe, Michele, 1981-. “Construção de conjuntos numéricos : dos números inteiros aos hiperreais: Construction of the numerical sets : from integer to hyperreal numbers.” 2016. Thesis, Universidade Estadual de Campinas. Accessed December 05, 2020. http://repositorio.unicamp.br/jspui/handle/REPOSIP/321576.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Calefe, Michele, 1981-. “Construção de conjuntos numéricos : dos números inteiros aos hiperreais: Construction of the numerical sets : from integer to hyperreal numbers.” 2016. Web. 05 Dec 2020.

Vancouver:

Calefe, Michele 1. Construção de conjuntos numéricos : dos números inteiros aos hiperreais: Construction of the numerical sets : from integer to hyperreal numbers. [Internet] [Thesis]. Universidade Estadual de Campinas; 2016. [cited 2020 Dec 05]. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/321576.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Calefe, Michele 1. Construção de conjuntos numéricos : dos números inteiros aos hiperreais: Construction of the numerical sets : from integer to hyperreal numbers. [Thesis]. Universidade Estadual de Campinas; 2016. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/321576

Not specified: Masters Thesis or Doctoral Dissertation

Universidade Estadual de Campinas

2.
Sperança, Llohann Dallagnol, 1986-.
Geometria e topologia *de* cobordos: Geometry and topology of cobondaries.

Degree: 2012, Universidade Estadual de Campinas

URL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/307262

Abstract: In this work we study the geometry and topology of manifolds homemorphic, but not diffeomorphic, to the standard sphere Sn, the so called exotic spheres. We realize two of these manifolds as isometric quotients of principal bundles with connection metrics over the constant curved sphere. Through this, we present symmetries in these spaces and explicit examples of diffeomorphisms not isotopic to the identity, using them for the calculation of equivariant homotopy groups. As another application, we prove that, if a homotopy 15-sphere is realizeble as the total space of a linear bundle over the standard 8-sphere, then, it is realizeble as the total space of a linear bundle over the exotic 8-sphere with the same transition maps. In the last chapter we deal with the geometry of pull-back bundles, deducing a necessary condition on the pull-back map for nonnegative curvature of the induced connection metric
*Advisors/Committee Members: UNIVERSIDADE ESTADUAL DE CAMPINAS (CRUESP), Rigas, Alcibiades, 1947- (advisor), Duran Fernandez, Carlos Eduardo, 1967- (coadvisor), Universidade Estadual de Campinas. Instituto de Matemática, Estatística e Computação Científica (institution), Programa de Pós-Graduação em Matemática (nameofprogram), Gorodski, Claudio (committee member), Ziller, Wolfgang (committee member), Jardim, Marcos Benevenuto (committee member), Barros, Tomas Edson (committee member).*

Subjects/Keywords: Topologia diferencial; Difeomorfismos; Submersões riemanianas; Variedades riemanianas; Geometria diferencial; Differential topology; Diffeomorphisms; Riemannian submersions; Riemannian manifolds; Differential geometry

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Sperança, Llohann Dallagnol, 1. (2012). Geometria e topologia de cobordos: Geometry and topology of cobondaries. (Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/307262

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Sperança, Llohann Dallagnol, 1986-. “Geometria e topologia de cobordos: Geometry and topology of cobondaries.” 2012. Thesis, Universidade Estadual de Campinas. Accessed December 05, 2020. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307262.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Sperança, Llohann Dallagnol, 1986-. “Geometria e topologia de cobordos: Geometry and topology of cobondaries.” 2012. Web. 05 Dec 2020.

Vancouver:

Sperança, Llohann Dallagnol 1. Geometria e topologia de cobordos: Geometry and topology of cobondaries. [Internet] [Thesis]. Universidade Estadual de Campinas; 2012. [cited 2020 Dec 05]. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/307262.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Sperança, Llohann Dallagnol 1. Geometria e topologia de cobordos: Geometry and topology of cobondaries. [Thesis]. Universidade Estadual de Campinas; 2012. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/307262

Not specified: Masters Thesis or Doctoral Dissertation

Universidade Estadual de Campinas

3.
Hoefel, Eduardo Outeiral Correa.
Espaço *de* configurações e OCHA: Configuration spaces and OCHA.

Degree: 2006, Universidade Estadual de Campinas

URL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/307207

Abstract: This thesis consists of the study of OCHA (Open-Closed Homotopy Algebras) from both the algebraic and geometric viewpoint. It essentially contains the proof of two new results. The first one is related to the definition of OCHA through coderivations. More specifically, it is shown that any degree one coderivation D E Caderl(Sc7íc 0 TC7ío) such that D2 = O defines an OCHA structure on 7í = 7íc E9 7ío. Where 7íc and 7ío are respectively the state spaces of Closed String Field Theory and apen String Field Theory. It was cIear since its definition in 2004 that OCHAs can be defined in terms of coderivations. Nevertheless, the fact that any such coderivation is of the OCHA form is new. The second result involves the relation between OCHA and the real version of the Fulton MacPherson compactification of the configuration space of points on the cIosed upper half-plane. That result shows the cIose relation between OCHAs and the Swiss-Cheese operad introduced by Voronov [411. Such relation was in fact suggested in the introductian of [141. Chapter 1 contains a discussion about the coalgebraic definition of OCHA and the above mentioned characterization of alI coderivations. It is also shown that OCHA can be obtained from certain A8 algebras, similarly to way in which Lie algebras are obtained fro_ associative algebras. Chapter 2 then shows how to approach OCHA using aperads. The space C(p, q) (the FuIton-MacPherson compactification of the configuration space of p + q points on the upper half-plane with p interior points and q boundary points) is discussed on chapter 3 and on chapter 4 it is shown that the essential part of the operad describing OCHA appears on the first line Of the spectral sequence induced by that space. In other words, we could say that the algebraic structure of OCHA is encoded in the stratification of C(p, q), since this space has the structure of a manifold with corners. The final chapter is a discussion about the meaning of the two mais results of this thesis. After that, some problems which could be explored by the student interested on homotopy algebras and related subjects are mentioned.
*Advisors/Committee Members: UNIVERSIDADE ESTADUAL DE CAMPINAS (CRUESP), Rigas, Alcibiades, 1947- (advisor), Barros, Tomas Edson (coadvisor), Universidade Estadual de Campinas. Instituto de Matemática, Estatística e Computação Científica (institution), Programa de Pós-Graduação em Matemática (nameofprogram), Spreafico, Mauro (committee member), Carvalho, Alexandre Luis Trovon de (committee member), Jardim, Marcos Benevenuto (committee member), Moura, Adriano Adrega de (committee member).*

Subjects/Keywords: Topologia algébrica; Teoria da homotopia; Teoria de módulos; Algebraic topology; Homotopy theory; Moduli theory; Homological algebra

Record Details Similar Records

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Hoefel, E. O. C. (2006). Espaço de configurações e OCHA: Configuration spaces and OCHA. (Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/307207

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Hoefel, Eduardo Outeiral Correa. “Espaço de configurações e OCHA: Configuration spaces and OCHA.” 2006. Thesis, Universidade Estadual de Campinas. Accessed December 05, 2020. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307207.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Hoefel, Eduardo Outeiral Correa. “Espaço de configurações e OCHA: Configuration spaces and OCHA.” 2006. Web. 05 Dec 2020.

Vancouver:

Hoefel EOC. Espaço de configurações e OCHA: Configuration spaces and OCHA. [Internet] [Thesis]. Universidade Estadual de Campinas; 2006. [cited 2020 Dec 05]. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/307207.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Hoefel EOC. Espaço de configurações e OCHA: Configuration spaces and OCHA. [Thesis]. Universidade Estadual de Campinas; 2006. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/307207

Not specified: Masters Thesis or Doctoral Dissertation