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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Orbits of higher-dimensional hereditarily indecomposable continua


Author: James T. Rogers
Journal: Proc. Amer. Math. Soc. 95 (1985), 483-486
MSC: Primary 54F20; Secondary 54F45, 54F50
MathSciNet review: 806092
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ X$ be a continuum. The following theorems are proved.

Theorem. If $ \dim X > 1$, then $ X$ contains uncountably many nonhomeomorphic continua.

Theorem. If $ \dim X > 1$ and $ X$ is hereditarily indecomposable, then $ X$ has uncountably many orbits under the action of its homeomorphism group.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0806092-1
PII: S 0002-9939(1985)0806092-1
Keywords: Continuum, homogeneous, aposyndetic, hereditarily equivalent, hereditarily indecomposable, dimension
Article copyright: © Copyright 1985 American Mathematical Society