On a question of B.J. Baker and M. Laidacker concerning disjoint compacta in $\mathbb R^N$

Abstract

We describe wild embeddings of polyhedra into R N which show that the answer to the question of B.J. Baker-M. Laidacker (1989) concerning uncountable families of pairwise disjoint compacta can be twofold. The central idea of our construction is the use of specific wild Cantor sets, namely, Antoine-Blankinship-Ivanov necklaces and Krushkal sticky sets. Our basic tools are Antoine's methods and Shtan'ko demension theory.

An answer to a question of J.W. Cannon and S.G. Wayment

“…To some extent, the possibility to find the desired sequences is explained by the fact that a small homeomorphism X 0 ∼ = X i may have no small extending homeomorphism R N ∼ = R N . Compare with [24,Thm. 4,Cor.…”