Intersection properties of typical compact sets

Abstract

We prove that a typical compact set does not contain any similar copy of a given pattern. We also prove that a typical compact set of $[0,1{]}^d(d\ge 2)$ intersects any $(d-1)$-dimensional plane in at most $d$ points. We study the "hitting probabilities" of compact sets in the sense of Baire category. In the end we study the arithmetic properties of typical compact sets in $[0,1]$ and the "hitting probabilities" of continuous functions.

12 pages

References in corpus (1)

• Locally rich compact sets