Uppeer semicontinuous decompositions E3 into subarc's of Bing's sling and points.

Abstract

Bing's sling is a simple closed curve in Euclidean 3-space E3 for which there is no homeomorphism h from E3 onto itself taking it to a circle. We say that Bing's sling is a wild simple closed curve. Any subarc A of Bing's sling is cellular that is, each neighbourhood of A contains a 3-cell which contains A in its interior. We study upper semicontinuous decompositions of euclidean 3-space E3 into points and pairwise disjoint subarcs of bing's sling. We prove that such decompositions always yields decomposition spaces that are homomorphic to E3. Chapter 1 deals with some basic concepts and results from decomposition space theory needed in subsequent chapters. Chapter 2 deals with the construction of Bing's sling and chapter 3 is devoted to the study of the special type of decomposition space of E³.