Rigid -dimensional compacta whose squares are manifolds

Authors:
Fredric D. Ancel, Paul F. Duvall and S. Singh

Journal:
Proc. Amer. Math. Soc. **88** (1983), 330-332

MSC:
Primary 54G20; Secondary 54B15, 55M15, 57P99

DOI:
https://doi.org/10.1090/S0002-9939-1983-0695269-2

MathSciNet review:
695269

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Abstract: A space is *rigid* if its only self-homeomorphism is the identity. In response to a question of Jan van Mill, Ancel and Singh have given examples of rigid -dimensional compacta, for each , whose squares are manifolds. We construct a rigid -dimensional compactum whose square is the manifold . In fact, we construct uncountably many topologically distinct compacta with these properties.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0695269-2

Keywords:
Cell-like compactum,
homogeneous,
manifold,
generalized -manifold,
cell-like decomposition

Article copyright:
© Copyright 1983
American Mathematical Society