An example of a doubling "inherently" infinite-dimensional subset of $l_2$
Andrea Schioppa
TL;DR
This paper constructs a doubling subset of l_2 that cannot be embedded into any finite-dimensional Euclidean space, addressing a question in metric geometry.
Contribution
It provides the first example of a doubling subset of l_2 that defies finite-dimensional biLipschitz embedding, answering a longstanding open question.
Findings
Constructed a doubling subset of l_2 with infinite-dimensional properties.
Proved the subset cannot be biLipschitz embedded into finite-dimensional Euclidean space.
Addresses a question posed by Lang and Plaut.
Abstract
We construct a doubling subset of which cannot be biLipschitz embedded in any finite dimensional Euclidean space. This answers a question of Lang and Plaut.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Mathematical Modeling in Engineering · Topological and Geometric Data Analysis