Characterization of quasi-orbit spaces

• Autores: Hawete Hattab
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 11, Nº 2, 2012, págs. 435-442
• Idioma: inglés
• DOI: 10.1007/s12346-011-0066-5
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• Resumen

  • Let G be a subgroup of the group Homeo(X) of homeomorphisms of a topological space X. The class of an orbit O of G is the union of all orbits having the same closure as O. We denote by X/G˜ the space of classes of orbits called the quasi-orbit space. The regular part of a T 0-space is the union of open subsets homeomorphic to R or to S1.

    The complementary of the regular part is called the singular part. In this paper we give a characterization of the topological spaces with finite singular parts and which are quasi-orbit spaces with respect to countable groups of the group of homeomorphisms of a one dimensional manifold.

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