Decomposition spaces having arbitrarily small neighborhoods with -sphere boundaries

Author:
Edythe P. Woodruff

Journal:
Trans. Amer. Math. Soc. **232** (1977), 195-204

MSC:
Primary 57A10; Secondary 54B15

DOI:
https://doi.org/10.1090/S0002-9947-1977-0442944-2

MathSciNet review:
0442944

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Abstract: Let *G* be an u.s.c. decomposition of . Let *H* denote the set of nondegenerate elements and *P* be the natural projection of onto . Suppose that each point in the decomposition space has arbitrarily small neighborhoods with 2-sphere boundaries which miss . We prove in this paper that this condition implies that is homeomorphic to . This answers a question asked by Armentrout [1, p. 15]. Actually, the hypothesis concerning neighborhoods with 2-sphere boundaries is necessary only for the points of .

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DOI:
https://doi.org/10.1090/S0002-9947-1977-0442944-2

Article copyright:
© Copyright 1977
American Mathematical Society