A Fundamental Theorem on Decompositions of the Sphere into Points and Tame Arcs
نویسندگان
چکیده
1. Introduction. R. H. Bing showed that an upper semicontinuous decomposition of £3 into points and tame arcs did not necessarily produce a decomposition space topologically equivalent to E3 [1J. M. L. Curtis and R. L. Wilder showed [2] that the decomposition space of Bing was a homotopy manifold, thus negatively answering a question proposed by Griffiths [3J. R. Rosen recently announced [4] a result which in part appears to be an example of E3 into points and tame arcs such that the decomposition space is not locally euclidean at any point. Thus, upper semicontinuous decompositions of E3 (or 53) into points and tame arcs yield various types of decomposition spaces. It is the purpose of this paper to prove a theorem which in particular implies that every upper semicontinuous decomposition of 53 into points and tame arcs yields a homotopy mani-fold decomposition space. Arguments employed here are completely elementary.
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