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Homogeneity and the disjoint arcs property

Author(s): Pawe\l Krupski
Journal: Proc. Amer. Math. Soc. 127 (1999), 1873-1876.
MSC (1991): Primary 54F15, 54F65, 57N05
Posted: February 17, 1999
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Abstract: Some previous results of the author towards a classification of homogeneous metric continua are improved. The disjoint arcs property is fully revealed in this context. In particular, closed $n$-manifolds, $n=1,2$, are characterized as those homogeneous continua which do not have the disjoint arcs property.

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Additional Information:

Pawe\l Krupski
Affiliation: Mathematical Institute, University of Wroclaw, Pl. Grunwaldzki 2/4, 50-384 Wro- claw, Poland
Email: krupski@math.uni.wroc.pl

DOI: 10.1090/S0002-9939-99-04682-1
PII: S 0002-9939(99)04682-1
Keywords: Homogeneous continuum, disjoint arcs property, two-manifold, solenoid, Sierpi\'{n}ski universal curve
Received by editor(s): December 3, 1996
Received by editor(s) in revised form: September 25, 1997
Posted: February 17, 1999
Additional Notes: This paper was presented at the 8th Prague Topological Symposium in August 1996
Dedicated: Dedicated to my wife Ewa
Communicated by: Alan Dow
Copyright of article: Copyright 1999, American Mathematical Society

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