Most Cantor sets in $\mathbb R^N$ are in general position with respect to all projections

TL;DR

This paper proves that most Cantor sets in Euclidean space are in general position relative to all projections, answering a question posed in 1994, and extends the discussion to the Hilbert space setting.

Contribution

It establishes a general position result for most Cantor sets in Euclidean and Hilbert spaces, addressing a long-standing open question.

Findings

Most Cantor sets in ^N are in general position with respect to all projections.

The result extends to the Hilbert space _2.

Answers a question of John Cobb from 1994.

Abstract

We prove the theorem stated in the title. This answers a question of John Cobb (1994). We also consider the case of the Hilbert space $\ell _2$.