Vol. 19, No. 3, 1966

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ISSN: 0030-8730
Sets with zero-dimensional kernels

Neal Eugene Foland and John M. Marr

Vol. 19 (1966), No. 3, 429–432
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
Authors
Neal Eugene Foland
John M. Marr