The strange aspect of most compacta

ZAMFIRESCU, Tudor

J. Math. Soc. Japan, Tome 57 (2005) no. 4, p. 701-708 / Harvested from Project Euclid

Résumé

In this paper we describe a compact set $K$ in $\mathbf{R}^d$ which is typical from the point of view of Baire categories, as it appears when seen from some point $x$ of $\mathbf{R}^d$ . It matters whether $x$ belongs to $K$ or not! If $x\not\in K$ , then $K$ looks porous (this is easily seen). If $x\in K$ , then $K$ looks only $\sigma$ -porous, but dense at least in a half-sphere (of directions from $x$ ). If $x$ is a typical point of $K$ , then $K$ looks even dense (in the whole sphere).

Détail

Publié le : 2005-07-14
Classification:  Baire categories,  compacta,  continua,  starshaped sets,  54E52,  54F15,  54D30