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Intersection properties of typical compact sets
- Publication Year :
- 2015
-
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 $[0,1]^{d} (d\geq 2)$ 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.<br />Comment: 12 pages
- Subjects :
- Mathematics - Classical Analysis and ODEs
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1512.04726
- Document Type :
- Working Paper