In this thesis, some characterizations of continua of finite degree are given. It turns out that being of finite degree (by formal definition) can be described by saying there exists an equivalent metric in which Hausdorff linear measure of the continuum is finite. I discuss this result in detail.

Orientador: Frab Norberto Boscolo / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Odontologia de Piracicaba / Made available in DSpace on 2018-07-22T03:21:57Z (GMT). No. of bitstreams: 1 Pereira_TeresaCristinaRangel_M.pdf: 2396331 bytes, checksum: 6560e28d5c00747cb15d69d307010e69 (MD5) Previous issue date: 1997 / Resumo: Este estudo teve como finalidades realizar uma análise comparativa entre duas técnicas radiográficas transcranianas com o auxílio do cefalostato ACCURAD-200, nas posições Padrão e Corrigida e desenvolver um gabarito que auxilie o profissional a medir os espaços articulares anterior e posterior, fornecendo informações sobre o posicionamento condilar. Foram radiografados 59 pacientes, numa faixa etária entre 18 e 35 anos, que voluntariamente se propuseram a participar deste estudo. Foi realizada uma radiografia ínfero-superior para a correção da incidência do feixe de raios X (posição Corrigida). Sobre as radiografias transcranianas foram realizados os traçados com o auxílio do gabarito e feitas as medidas lineares dos espaços articulares, usando para tal um paquímetro digital. Nossos resultados demonstraram que para ambas as técnicas empregadas o espaço articular posterior apresentou-se menor que o anterior, e que o método desenvolvido permite a avaliação do posicionamento condilar / Abstract: This study had the purpose of making a comparative analyse between transcranial radiographs utilizing ACCURAD-200 headholder in standard and corrected positions and to develop a Template to help professionals measure the anterior and posterior joint spaces and give some information about condyle position. Transcranial radiographs were taken from 59 voluntaries who participated in this study, aged between 18-35 years. A submental-vertex radiograph was obtained to correct the direction of X-rays (corrected position). A drawn was made over the films whith help of the Template and the linear measure of the joint space was made with a digital pachymeter. The results have shown that for both technics used the posterior joint space was smaller than the anterior one, and the method developed permitted the estimation of condylar positioning / Mestrado / Radiologia / Mestre em Odontologia

The notion of a curve played important role in the history of mathematical thought. This dissertation is focused on the conception of a curve in analysis, point set theory and topology. The rectification of curves and the notion of arc length are considered in connection with the history of analysis from antiquity to the beginning of the 20th century. "Measurement of curves" is also discussed from the measure-theoretic viewpoint and various definitions of linear measure and fractional dimension are described. Historically, there are two main approaches to understanding curves. Jordan defined a curve as a continuous image of a closed interval. However, his definition appeared to be too wide, since it was met by objects such as the Peano curve. In the point set theory, a curve is considered to be a one-dimensional continuum. The development of the dimension theory and the continuum theory, starting with the pioneering work of Bolzano, was motivated by the search for rigorous topological definition of a curve, a surface etc. Among "pathological" curves, that were often introduced as counterexamples in the development of modern analysis, we can find early examples of fractals. The fractal theory motivated further study of mathematical properties of these curves in the late 20th century, such as self-similarity and...