Vol. 33, No. 3, 1970

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Wild points of cellular arcs in 2-complexes in E3 and cellular hulls

Gail Atneosen

Vol. 33 (1970), No. 3, 551–553

Loveland has established that if W is the set of wild points of a cellular arc that lies on a 2-sphere in E8, then either W is empty, W is degenerate, or W contains an arc. This note considers 2-complexes rather than 2-spheres. Making strong use of Loveland’s results and others, it is proved that a cellular arc in a 2-complex in E8 either contains an arc of wild points or has at most one wild point that has a neighborhood in the 2-complex homeomorphic to an open 2-cell. In the case of noncellular arcs in E3, one can investigate “minimal cellular sets” containing the arc. A cellular hull of a subset A of Es is a cellular set containing A such that no proper cellular set also contains A. A characterization is given of those arcs in E3 that have cellular hulls that lie in tame 2-complexes in E3.

Mathematical Subject Classification
Primary: 54.78
Received: 22 October 1969
Published: 1 June 1970
Gail Atneosen