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Let G ⊂ Homeo(E) be a group of homeomorphisms of a topological space E. The class of an orbit O of G is the union of all orbits having the same closure as O. Let E/G̃ be the space of classes of orbits, called the quasi-orbit space. We show that every second countable T₀-space Y is a quasi-orbit space E/G̃, where E is a second countable metric space. The regular part X₀ of a T₀-space X is the union of open subsets homeomorphic to ℝ or to 𝕊¹. We give a characterization of the spaces X with finite...
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