Vol. 50, No. 2, 1974

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Vertically countable spheres and their wild sets

Lowell Duane Loveland

Vol. 50 (1974), No. 2, 521–529

A 2-sphere S in E3 is said to have vertical order n if the intersection of each vertical line with S contains no more than n points. It is shown that S IntS is a 3-cell that is locally tame from ExtS modulo a 0-dimensional set if S has vertical order 5. A subset X of E3 is said to have countable (finite) vertical order if the intersection of X with each vertical line consists of countably (finitely) many points. A 2-sphere in Es with countable vertical order can have a wild set of dimension no larger than one.

Mathematical Subject Classification
Primary: 57A10
Received: 21 November 1972
Published: 1 February 1974
Lowell Duane Loveland