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

DOI: 10.2140/pjm.1970.33.555

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