Vol. 33, No. 3, 1970

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On embeddings of 1-dimensional compacta in a hyperplane in E4

John Logan Bryant and De Witt Sumners

Vol. 33 (1970), No. 3, 555–557
Abstract

In this note a proof of the fbllowing theorem is given. THEOREM 1. Suppose that X is a l-dimensional compactum in a 3-dimensional hyperplane E3 in euclidean 4-space E4, that 𝜖 > 0, and that f : X E8 is an embedding such that d(x,f(x)) < 𝜖 for each x X. Then there exists an 𝜖-push h of (E4,X) such that h|X = f.

Mathematical Subject Classification
Primary: 54.78
Secondary: 55.00
Milestones
Received: 5 November 1969
Published: 1 June 1970
Authors
John Logan Bryant
Department of Mathematics
Florida State University
Tallahassee FL 32306
United States
De Witt Sumners