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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A homogeneous continuum that is non-Effros
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by David P. Bellamy and Kathryn F. Porter PDF
Proc. Amer. Math. Soc. 113 (1991), 593-598 Request permission

Abstract:

Using a very geometric, intuitive construction, an example is given of a homogeneous, compact, connected Hausdorff space $(X,T)$ that does not satisfy the conclusion of the Effros Theorem. In particular, there is a point $p$ and a neighborhood $V$, of the identity in the group of self-homeomorphisms on $X$, with the compact-open topology such that ${V_p} = \{ h(p):h \in V\}$ is nowhere dense in $X$.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 113 (1991), 593-598
  • MSC: Primary 54C35; Secondary 54F15, 54H13, 57S05
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1070510-X
  • MathSciNet review: 1070510