Abstract
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 \({X/\widetilde{G}}\) 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 \({\mathbb{R}}\) or to \({\mathbb{S}^1.}\) 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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Hattab, H. Characterization of quasi-orbit spaces. Qual. Theory Dyn. Syst. 11, 435–442 (2012). https://doi.org/10.1007/s12346-011-0066-5
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DOI: https://doi.org/10.1007/s12346-011-0066-5