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http://hdl.handle.net/11154/1148
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Title: | (1)(2)-Homogeneous continua with cut points |
Authors: | Nadler, SB Pellicer-Covarrubias, P Puga, I |
Issue Date: | 2007 |
Abstract: | A space is said to be _21-homogeneous provided that there are exactly two orbits for the action of the group of homeomorphisms of the space onto itself. It is shown that if X is a 1/2-homogeneous continuum with at least one cut point, then X has either uncountably many cut points or only one cut point c. In the former case, X is 1/2-homogeneous if and only if X is an arc or X is a compactification of the reals R-1 whose remainder is the union of two disjoint, nondegenerate, homeomorphic homogeneous continua and the ends of X are mutually homeomorphic and 1/3-homogeneous. In the latter case, the closures of the components of X - {c} are mutually homeomorphic and 2-homogeneous at c, and ord(c)(X) >= 4 furthermore, if ord(c)(X) <= omega, X is a locally connected bouquet of simple closed curves. Conversely, the two conditions about the components of X - {c} are shown to imply X is 1/2-homogeneous under an additional assumption, which is shown by examples to be both required and restrictive. (C) 2007 Elsevier B.V. All rights reserved. |
URI: | http://hdl.handle.net/11154/1148 |
ISSN: | 0166-8641 |
Appears in Collections: | Matemáticas
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