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 | References | Similar Articles | Additional Information

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]**Fredric D. Ancel,*An alternative proof and applications of a theorem of E. G. Effros*, Michigan Math. J.**34**(1987), no. 1, 39–55. MR**873018**, 10.1307/mmj/1029003481**[2]**Richard Arens,*Topologies for homeomorphism groups*, Amer. J. Math.**68**(1946), 593–610. MR**0019916****[3]**Richard F. Arens,*A topology for spaces of transformations*, Ann. of Math. (2)**47**(1946), 480–495. MR**0017525****[4]**Edward G. Effros,*Transformation groups and 𝐶*-algebras*, Ann. of Math. (2)**81**(1965), 38–55. MR**0174987****[5]**R. L. Moore,*Foundations of point set theory*, Revised edition. American Mathematical Society Colloquium Publications, Vol. XIII, American Mathematical Society, Providence, R.I., 1962. MR**0150722****[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:
http://dx.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