New examples in dimensions N ≥ 4 related to a question of J. W. Cannon and S. G. Wayment

Abstract

Solving R. J. Daverman’s problem, V. S. Krushkal described sticky Cantor sets in [Formula: see text] for [Formula: see text]. Such sets cannot be isotoped off themselves by small ambient isotopies. Using Krushkal sets, we present a new series of wild embeddings related to a question of J. W. Cannon and S. G. Wayment (1970). Namely, for [Formula: see text], we construct examples of compacta [Formula: see text] with the following two properties: some sequence [Formula: see text] converges homeomorphically to [Formula: see text], but no uncountable family of pairwise disjoint sets [Formula: see text] exists such that each [Formula: see text] is ambiently homeomorphic to [Formula: see text].