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A generalization of 2-homogeneous continua being locally connected

Author: Keith Whittington
Journal: Proc. Amer. Math. Soc. 126 (1998), 3131-3132
MSC (1991): Primary 54F15
MathSciNet review: 1616577
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Abstract: An elementary proof is given that if each pair of points of a homogeneous metric continuum can be mapped by a homeomorphism into an arbitrarily small connected set, then the continuum is locally connected.

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

  • 1. C. E. Burgess, Homogeneous continua, Summary of Lectures and Seminars, Summer Institute on Set Theoretic Topology, University of Wisconsin (1955), 75-78.
  • 2. E. G. Effros, Transformation groups and C*-algebras, Ann. of Math. (2) 81 (1965), 38-55. MR 30:5175
  • 3. G. S. Ungar, On all kinds of homogeneous spaces, Trans. Amer. Math. Soc. 212 (1975), 393-401. MR 52:6684

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Additional Information

Keith Whittington
Affiliation: Department of Mathematics, University of the Pacific, Stockton, California 95211

Keywords: Homogeneous, locally connected
Received by editor(s): January 30, 1998
Received by editor(s) in revised form: March 19, 1998
Communicated by: Alan Dow
Article copyright: © Copyright 1998 American Mathematical Society

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