# An example of a doubling "inherently" infinite-dimensional subset of $l_2$

## 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.

## Key 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 $l_2$ which cannot be biLipschitz embedded in any finite dimensional Euclidean space. This answers a question of Lang and Plaut.

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Source: https://tomesphere.com/paper/1703.10265