A characterization of tame curves in three-space

Abstract

points. Property ?P has been extended to 2-cells and 3-cells [6], and it was found that if a 1-cell, 2-cell, or 3-cell has two of the three properties; the uniform disk property, property ?P, and the strong enclosure property, then it also has the third. The principal result obtained here is that a 2-cell in 3-space is tame if and only if it has both the strong enclosure property and the hereditary disk property. This implies that a surface C, i.e., a 2-manifold with or without boundary, is locally tame at a point p if and only if p lies on the interior of a sub-disk of C with these two properties. Both Bing [3] and Moise [11] have shown that locally tame closed sets are tame, so the above