ABSTRACT
A continuum is a compact, connected metric space; a Hausdorff continuum is a compact, connected Hausdorff_space. For any topological space, S, and for any A C S, we shall use_A to denote the closure of A in S. The boundary of A in S is the set A D S — A, and is denoted by Bd(A) when S is the largest space under consideration. Finally, if A and B are subsets of S such that A n B ^ 0, then we shall say that A bumps B; otherwise, we shall say that A is far from B. We note that tiACB, then A bumps Bd(B) if and only if A n S-B ^ 0.
