On embeddings of compacta in Euclidean space
John Bryant · Proceedings of the American Mathematical Society · 1969
In [5] it was shown that any two embeddings of a k-dimensional compact absolute neighborhood retract into euclidean n-space, En(n > 5 and 2k+2 <n), are equivalent by an ambient isotopy of En, provided the complement of each embedding is uniformly locally 1-connected (abbreviated 1-ULC). The purpose of this paper is to prove a generalization of the result stated above for embeddings of arbitrary compacta in En. The following theorem is the main result.