Vol. 48, No. 2, 1973

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Decompositions of E3 into points and countably many flexible dendrites

Richard Snay

Vol. 48 (1973), No. 2, 503–509

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.

Mathematical Subject Classification 2000
Primary: 57A15
Secondary: 54F50
Received: 14 July 1972
Revised: 11 December 1972
Published: 1 October 1973
Richard Snay