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

 

A homogeneous continuum that is non-Effros


Authors: David P. Bellamy and Kathryn F. Porter
Journal: Proc. Amer. Math. Soc. 113 (1991), 593-598
MSC: Primary 54C35; Secondary 54F15, 54H13, 57S05
MathSciNet review: 1070510
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1070510-X
PII: S 0002-9939(1991)1070510-X
Keywords: Homogeneous, Effros' Theorem, compact-open topology, continuum, monotone map, group of self-homeomorphisms, complemented compact-open topology
Article copyright: © Copyright 1991 American Mathematical Society