Vol. 82, No. 1, 1979

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The dimension of the kernel of a planar set

Marilyn Breen

Vol. 82 (1979), No. 1, 15–21
Abstract

Let S be a compact subset of R2. We establish the following: For 1 k 2, the dimension of ker S is at least k if and only if for some 𝜖 > 0, every f(k) points of S see via S a common k-dimensional neighborhood having radius 𝜖, where f(1) = 4 and f(2) = 3. The number f(k) in the theorem is best possible.

Mathematical Subject Classification 2000
Primary: 52A30
Secondary: 52A35
Milestones
Received: 15 January 1978
Published: 1 May 1979
Authors
Marilyn Breen