Vol. 58, No. 1, 1975

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

Edythe Parker Woodruff

Vol. 58 (1975), No. 1, 291–295

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
Published: 1 May 1975
Edythe Parker Woodruff