Sets with zero-dimensional kernels

Neal Eugene Foland and John M. Marr

Vol. 19 (1966), No. 3, 429–432

DOI: 10.2140/pjm.1966.19.429

Abstract

F. A. Valentine in his book ([1], p. 177, Problem 6.5) suggests that a sufficient condition for a nonempty compact and connected subset S of E² to have a kernel consisting of a single point is that each triple of points of S can see via S a unique point of S. The authors show that this condition is sufficient if S is any subset of a topological linear space which contains a noncollinear triple.

Mathematical Subject Classification

Primary: 52.30

Milestones

Received: 18 June 1965

Published: 1 December 1966