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13 - Applications in Embedding Theory

from Part Three - Applications

Published online by Cambridge University Press:  13 October 2020

Jonathan M. Fraser
Jonathan M. Fraser
Affiliation:
University of St Andrews, Scotland
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Summary

Even though the Assouad dimension appeared in other contexts, it was the pioneering work of Assouad in the 1970s which served to popularise the notion and establish its deep connections with several areas of mathematics, most notably embedding theory. In this chapter we discuss various problems in embedding theory, all of which can be understood as asking for conditions on a metric space guaranteeing the existence of an injection (the embedding) into Euclidean space.

Keywords

Assouad's embedding theoremdoubling metricuniformly perfectspiral winding problemalmost bi-Lipschitz embedding
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Chapter
Information
Assouad Dimension and Fractal Geometry , pp. 197 - 214
Publisher: Cambridge University Press
Print publication year: 2020

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