Orbits of higher-dimensional hereditarily indecomposable continua

Rogers, James T.

doi:10.1090/S0002-9939-1985-0806092-1

Orbits of higher-dimensional hereditarily indecomposable continua
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Proc. Amer. Math. Soc. 95 (1985), 483-486 Request permission

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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Sur un problème de M. H. Hahn

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