Closed subsets of Euclidean spaces contained in hereditarily indecomposable continua

Abstract

In this paper we prove that if A is a compact subset of the Euclidean space Rk (k≥3) with the property that every nondegenerate component of A is hereditarily indecomposable and A does not separate Rk, then there exists a hereditarily indecomposable subcontinuum M of Rk such that A⊂M. This proves a conjecture by D.P. Bellamy.