A map of E³ onto E³ taking no disk onto a disk

Edythe Parker Woodruff

Vol. 58 (1975), No. 1, 291–295

DOI: 10.2140/pjm.1975.58.291

Abstract

An example is given of an u.s.c. decomposition in which no disk in E³ maps onto a disk under the natural projection map P, and, furthermore, the decomposition space E³∕G is homeomorphic to E³. Each nondegenerate element is a tame arc. The image P(H) of the set of nondegenerate elements is 0-dimensional, although Cl P(H) is E³. The basic construction used is called a knit Cantor set of nondegenerate elements.

Mathematical Subject Classification

Primary: 57A10

Milestones

Published: 1 May 1975