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A note on group invariant continua

Published online by Cambridge University Press:  09 April 2009

William J. Gray
William J. Gray
Affiliation:
University of Alabama
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Let (X, T, π) be a topological transformation group, where X is a Hausedorff continuum. We will say that X is irreducibly T-invariant if no proper subcontinuum of X is T-invariant. Wallace, [6], has shown that if T is abelian and X is irreducibly T-invariant, then X has no cut point; he then asked if this statement remains true if “abelian” is replaced by “compact”. In this paper we answer this question in the affirmative, and prove a related result when T satisfies a recursive property.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 2 , May 1968 , pp. 310 - 312
Copyright
Copyright © Australian Mathematical Society 1968

References

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