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http://hdl.handle.net/11154/1167
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Title: | Cones that are 1/2-homogeneous |
Authors: | Nadler, SB Pellicer-Covarrubias, P |
Issue Date: | 2007 |
Abstract: | A space is 1/2-homogeneous provided that there are exactly two orbits for the action of 2 the group of homeomorphisms of the space onto itself. Let X be a nonempty compact metric space such that the cone over X is 1/2-homogeneous. It is shown that if X is finite-dimensional, then X is an absolute neighborhood retract. A general theorem is proved which shows that finite dimensionality is necessary. It is shown that if X is a 1-dimensional continuum or if X does not contain certain types of triods in some nonempty open set, then X is an arc or a simple closed curve (assuming Cone(X) is 1/2-homogeneous). A number of corollaries are derived. Some unanswered questions are stated. |
URI: | http://hdl.handle.net/11154/1167 |
ISSN: | 0362-1588 |
Appears in Collections: | Matemáticas
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