## 5 Citations

Geometric analysis on Cantor sets and trees

- Mathematics
- 2017

dUsing uniformization, Cantor type sets can be regarded as boundaries of rooted trees. In this setting, we show that the trace of a first-order Sobolev space on the boundary of a regular rooted tre…

Approximating spaces of Nagata dimension zero by weighted trees

- Mathematics
- 2021

Let X be a metric space which has Nagata dimension zero with constant c. We show that there exists a weighted tree which is 8c-bilipschitz equivalent to a dense subset of X. It turns out that for c =…

Quasi-symmetric invariant properties of Cantor metric spaces

- MathematicsAnnales de l'Institut Fourier
- 2019

For metric spaces, the doubling property, the uniform disconnectedness, and the uniform perfectness are known as quasi-symmetric invariant properties. The David-Semmes uniformization theorem states…

A Novel Proof of the Heine-Borel Theorem

- Mathematics
- 2008

Every beginning real analysis student learns the classic Heine-Borel theorem, that the interval (0,1) is compact. In this article, we present a proof of this result that doesn't involve the standard…

On $p$-metric spaces and the $p$-Gromov-Hausdorff distance

- Mathematics
- 2019

For each given p ∈ [1,∞] we investigate certain sub-family Mp of the collection of all compact metric spaces M which are characterized by the satisfaction of a strengthened form of the triangle…

## References

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- Mathematics
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These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.

Another introduction to the geometry of metric spaces

- Mathematics
- 2007

Here Lipschitz conditions are used as a primary tool, for studying curves in metric spaces in particular.

Metric Space

- MathematicsEncyclopedia of Database Systems
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In this chapter three subsequent studies of the determinants of infectious disease in eight operation rooms of the immune system are studied.

Elementary aspects of the geometry of metric spaces

- Mathematics
- 2007

The setting of metric spaces is very natural for numerous questions concerning manifolds, norms, and fractal sets, and a few of the main ingredients are surveyed here.

P-Adic Numbers: An Introduction

- Mathematics
- 1993

1 Aperitif.- 1 Aperitif.- 1.1 Hensel's Analogy.- 1.2 Solving Congruences Modulopn.- 1.3 Other Examples.- 2 Foundations.- 2.1 Absolute Values on a Field.- 2.2 Basic Properties.- 2.3 Topology.- 2.4…

Fourier Analysis on Local Fields.

- Mathematics
- 1975

This book presents a development of the basic facts about harmonic analysis on local fields and the "n"-dimensional vector spaces over these fields. It focuses almost exclusively on the analogy…

Principles of mathematical analysis

- Mathematics
- 1964

Chapter 1: The Real and Complex Number Systems Introduction Ordered Sets Fields The Real Field The Extended Real Number System The Complex Field Euclidean Spaces Appendix Exercises Chapter 2: Basic…

Introduction to Analysis

- Mathematics
- 1970

Cloth $85.00 “ Gunning’s book is a great introduction to analysis that presents precisely what an honors analysis course should include. The writing is rigorous but lively, and much interesting…

On dimension theory

- Education, Psychology
- 1969

What do you do to start reading dimension theory? Searching the book that you love to read first or find an interesting book that will make you want to read? Everybody has difference with their…