Closed subsets of Euclidean spaces contained in hereditarily indecomposable continua

摘要

In this paper we prove that if A is a compact subset of the Euclidean space R-k (k >= 3) with the property that every nondegenerate component of A is hereditarily indecomposable and A does not separate R-k, then there exists a hereditarily indecomposable subcontinuum M of R-k such that A subset of M. This proves a conjecture by D.P. Bellamy. (C) 2015 Elsevier B.V. All rights reserved.