Closed subsets of Euclidean spaces contained in hereditarily indecomposable continua

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