Dissertation--München Universität, 2002. / Notes bibliogr.

Inaug.-diss.--Freiburg i. Br. / Lebenslauf.

Inaug.-diss.--Freiburg i. Br. / Lebenslauf.

No description available.

Este trabalho está preocupado com o conceito de medida e dimensão de Hausdorff usando ferramentas matemáticas adequadas. Como, frequentemente, é importante e difícil determinar a dimensão Hausdorff 1 de um conjunto e ainda mais difícil de encontrar ou mesmo estimar a sua medida Hausdorff, por auto proteção é usado o conjunto ternário de Cantor. A construção ternária simplifica certas dificuldades técnicas sobre a teoria da dimensão. O conjunto de Cantor é um exemplo interessante de um conjunto magro, perfeito, compacto e não enumerável, cuja medida e dimensão topológica são nulas. A análise de muitas das suas propriedades e consequências interessantes nos campos da teoria dos conjuntos e da topologia nos oferece uma rota direta que leva à medida Hausdorff do conjunto Cantor e sua dimensão fractal que é igual à sua dimensão Hausdorff. Também é calculada a dimensão Hausdorff para alguns fractais clássicos, como o tapete Sierpinski e a curva de flocos de neve von Koch. / This work is concerned with the concept of Hausdorff measure and dimension using suitable mathematical tools. Since it is often important and dificult to determine the Hausdorff dimension2 of a set and even harder to find or even to estimate its Hausdorff measure, by self-protection choices, it is used the ternary Cantor set. The ternary construction reduces technical difficulties about dimension theory. Cantor set is an interesting example of a meager, perfect, compact, uncountable set whose measure and topologic dimension are zero. Analysis of many of its interesting properties and consequences in the fields of set theory and topology provides a direct route that leads to the Hausdorff measure of the Cantor set and its fractal dimension that is equal to its Hausdorff dimension. It is also computed the Hausdorff dimension for some classical fractals such as the Sierpinski carpet and the von Koch snowflake curve.

This thesis covers the Cantor Ternary Set and generalizations of the Cantor Set, and gives a complete existential theory for three set properties: denumerability, exhaustibility, and zero measure.

O objetivo deste trabalho é apresentar o cálculo das partições para espaços topológicos. Essa área trata do estudo de resultados do seguinte tipo: \"dados os espaços topológicos X e Y, um número natural n e um cardinal kappa, para qualquer que seja a partição de [X]^n em kappa pedaços, existe um subespaço H de X homeomorfo ao Y tal que [H]^n está contido num mesmo pedaço\". Iremos estudar esse tipo de afirmação, principalmente no caso em que n = 1 e Y é igual a um ordinal enumerável ou igual ao omega_1. Também veremos resultados que envolvem o cubo de Cantor. / The purpose of this work is to present the partition calculus for topological spaces. This area deals with the study of results of the following type: \"given the topological spaces X and Y, a natural number n and a cardinal number kappa, for whatever the partition of [X]^n into kappa pieces, there is a subspace H of X homeomorphic to Y such that [H]^n is contained in the same piece\". We will study results of this type mainly in the case where n = 1 and Y is a countable ordinal or the omega_1. We will also see results involving the Cantor cube.

Xiao, Chang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 37-[38]). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

Li, Chung Fai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 43). / Abstracts in English and Chinese. / Acknowledgement --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Construction of the State Spaces --- p.5 / Chapter 2.1 --- The Sierpinski Gasket --- p.5 / Chapter 2.1.1 --- Neighbourhood in the Sierpinski Gasket --- p.7 / Chapter 2.2 --- The Sierpinski Carpet --- p.9 / Chapter 2.2.1 --- Neighbourhood in the Sierpinski Carpet --- p.10 / Chapter 3 --- Preliminary Random Processes on Each Level --- p.12 / Chapter 3.1 --- The Sierpinski Gasket --- p.12 / Chapter 3.1.1 --- Definitions --- p.12 / Chapter 3.1.2 --- Properties of the Random Walk --- p.13 / Chapter 3.1.3 --- Preparations for convergence and continuity --- p.16 / Chapter 3.2 --- The Sierpinski Carpet --- p.19 / Chapter 3.2.1 --- The Brownian Motion Bn on Cn --- p.19 / Chapter 3.2.2 --- Properties of Bm(t) --- p.20 / Chapter 3.2.3 --- Exit time for Bn --- p.27 / Chapter 4 --- The limiting process --- p.29 / Chapter 4.1 --- The Sierpinski Gasket --- p.29 / Chapter 4.1.1 --- Convergence and continuity --- p.29 / Chapter 4.1.2 --- Extension from to G --- p.31 / Chapter 4.1.3 --- Markov property --- p.33 / Chapter 4.2 --- The Sierpinski Carpet --- p.34 / Chapter 4.2.1 --- Continuity --- p.34 / Chapter 4.2.2 --- Existence of Markov process on C --- p.37 / Chapter 4.2.3 --- Piecing Together --- p.38 / Bibliography --- p.43

No description available.