Krasnosel'skii Theorems for Non-Separating Compact Sets

Abstract

AbstractLet S ⊂ Rd, d ≥ 2, be compact and let E denote the set (d — 2) — extreme points of S. M. Breen has shown that if E is countable and S ≠ E, then S is planar. A new proof of this result is given as well as a Krasnosl'skii theorem for (d - 2) extreme points which combines and generalizes previous results.