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

DOI:
https://doi.org/10.1090/S0002-9939-1991-1070510-X

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 that does not satisfy the conclusion of the Effros Theorem. In particular, there is a point and a neighborhood , of the identity in the group of self-homeomorphisms on , with the compact-open topology such that is nowhere dense in .

**[1]**F. D. Ancel,*An alternative proof and applications of a theorem of E. G. Effros*, Michigan Math. J.**34**(1987), 39-55. MR**873018 (88h:54058)****[2]**R. F. Arens,*Topologies for homeomorphism groups*, Amer. J. Math.**68**(1946), 593-610. MR**0019916 (8:479i)****[3]**-,*A topology for spaces of transformations*, Ann. of Math. (2)**47**(1946), 480-495. MR**0017525 (8:165e)****[4]**E. G. Effros,*Transformation groups and**-algebras*, Ann. of Math. (2)**81**(1965), 38-55. MR**0174987 (30:5175)****[5]**R. L. Moore,*Foundations of point set theory*, Amer. Math. Soc. Colloq. Publ., vol. XIII, rev. ed., Amer. Math. Soc, Providence, RI, 1962. MR**0150722 (27:709)****[6]**K. F. Porter,*Evaluation maps on groups on self-homeomorphisms*, Ph.D. Dissertation, University of Delaware, 1987.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1070510-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