Vol. 49, No. 1, 1973

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Cross-sections of decompositions

John Philip Riley Jr.

Vol. 49 (1973), No. 1, 219–221

The following question was raised by R. H. Bing: “Is it true that if G is a monotone decomposition of E8 into straight line intervals and one-point sets, then ES∕G is homeomorphic to E3?” In his paper “Point-like decompositions of E8” he described a possible counter example. This example has the interesting property that it has many tame cross-sections, but if its decomposition space is homeomorphic to E8, its set of nondegenerate elements would have to form a wild Cantor set. This suggests that it would be interesting to study the connection between the embedding of a cross-section and the embedding of the set of nondegenerate elements in the decomposition space.

Mathematical Subject Classification 2000
Primary: 57A10
Secondary: 54B15
Received: 16 May 1972
Revised: 30 September 1972
Published: 1 November 1973
John Philip Riley Jr.