Rigid finite-dimensional compacta whose squares are manifolds

Authors:
Fredric D. Ancel and S. Singh

Journal:
Proc. Amer. Math. Soc. **87** (1983), 342-346

MSC:
Primary 54G20; Secondary 55M15, 57P99

DOI:
https://doi.org/10.1090/S0002-9939-1983-0681845-X

MathSciNet review:
681845

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Abstract | References | Similar Articles | Additional Information

Abstract: A space is *rigid* if its only self-homeomorphism is the identity. We answer questions of Jan van Mill by constructing for each , , a rigid -dimensional compactum whose square is homogeneous because it is a manifold. Moreover, for each , , we give uncountably many topologically distinct such examples. Infinite-dimensional examples are also given.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0681845-X

Keywords:
Generalized -manifold,
decomposition spaces,
homology spheres,
homogeneous,
cell-like decomposition

Article copyright:
© Copyright 1983
American Mathematical Society