Degree of homogeneity on cones (Q401450)
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scientific article; zbMATH DE number 6334612
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Degree of homogeneity on cones |
scientific article; zbMATH DE number 6334612 |
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Degree of homogeneity on cones (English)
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27 August 2014
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cone
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continuum
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degree of homogeneity
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local dendrite
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orbit
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1/2-homogeneous
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1/n-homogeneous
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The authors study the degree of homogeneity of the cone of a space \(X\) (the degree of homogeneity of a space \(X\) is the number of orbits for the action of the group of homeomorphisms of \(X\) onto itself).NEWLINENEWLINEThey determine the orbits and the degree of homogeneity of the cone of a space \(X\) in terms of that of \(X\), when \(X\) is either a local dendrite or a Hausdorff space with no arcs. They also analyze how some subsets of \({Cone}(X)\) behave under homeomorphisms of \({Cone}(X)\) onto itself.NEWLINENEWLINEThe paper ends with some open questions regarding the degree of homogeneity for some other classes of continua related to the ones that were studied in it.
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