Rigid finite-dimensional compacta whose squares are manifolds

Ancel, Fredric D.; Singh, S.

doi:10.1090/S0002-9939-1983-0681845-X

Rigid finite-dimensional compacta whose squares are manifolds
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by Fredric D. Ancel and S. Singh

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

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

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Abstract:

A space is rigid if its only self-homeomorphism is the identity. We answer questions of Jan van Mill by constructing for each $n$, $4 \leqslant n < \infty$, a rigid $n$-dimensional compactum whose square is homogeneous because it is a manifold. Moreover, for each $n$, $4 \leqslant n < \infty$, we give uncountably many topologically distinct such examples. Infinite-dimensional examples are also given.

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