Let G be an upper
semicontinuous decomposition of E3 whose only nondegenerate elements are
countably many dendrites. It has been asked by Armentrout whether it is
sufficient that each dendrite be tame in E3 in order that the decomposition
space E3|G be homeomorphic to E3. In Theorem 3 the sufficiency of the
tameness condition is shown as well as the sufficiency of the weaker condition
that each dendrite be flexible in E3. Theorem 2 states that if A and B are
flexible dendrites in E3 whose intersection is a point, then A ∪ B is a flexible
dendrite. This result is used to construct flexible dendrites in E3 which are not
tame.
