Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- PART I FINITE-DIMENSIONAL SETS
- 1 Lebesgue covering dimension
- 2 Hausdorff measure and Hausdorff dimension
- 3 Box-counting dimension
- 4 An embedding theorem for subsets of ℝN in terms of the upper box-counting dimension
- 5 Prevalence, probe spaces, and a crucial inequality
- 6 Embedding sets with dH(X − X) finite
- 7 Thickness exponents
- 8 Embedding sets of finite box-counting dimension
- 9 Assouad dimension
- PART II FINITE-DIMENSIONAL ATTRACTIORS
- Solutions to exercises
- References
- Index
4 - An embedding theorem for subsets of ℝN in terms of the upper box-counting dimension
from PART I - FINITE-DIMENSIONAL SETS
Published online by Cambridge University Press: 10 January 2011
Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- PART I FINITE-DIMENSIONAL SETS
- 1 Lebesgue covering dimension
- 2 Hausdorff measure and Hausdorff dimension
- 3 Box-counting dimension
- 4 An embedding theorem for subsets of ℝN in terms of the upper box-counting dimension
- 5 Prevalence, probe spaces, and a crucial inequality
- 6 Embedding sets with dH(X − X) finite
- 7 Thickness exponents
- 8 Embedding sets of finite box-counting dimension
- 9 Assouad dimension
- PART II FINITE-DIMENSIONAL ATTRACTIORS
- Solutions to exercises
- References
- Index
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- Dimensions, Embeddings, and Attractors , pp. 41 - 46Publisher: Cambridge University PressPrint publication year: 2010