ABSTRACT
The following theorem is proved in [2] in response to a question of J. B. Pugate (Problem 113 of the Houston Problem Book [1]). Theorem 1. Suppose M is a continuum. The following are equivalent.
1. The continuum M is irreducible about a finite set of points. 2. Every pair-wise disjoint collection of non-separating open subsets
of M is finite. 3. The continuum M is not the union of a countable monotonic col-
lection of its proper subcontinua. 4. The continuum M does not have infinitely many weakly non-sepa-
rating subcontinua each of which has an interior point that fails to lie in the closure of the union of the others.
