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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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$.


References [Enhancements On Off] (What's this?)

  • [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.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54C35, 54F15, 54H13, 57S05

Retrieve articles in all journals with MSC: 54C35, 54F15, 54H13, 57S05


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