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Displaying similar documents to “Groups of homeomorphisms and normal subgroups of the group of permutations.”

Topological conjugation classes of tightly transitive subgroups of Homeo₊(ℝ)

Enhui Shi, Lizhen Zhou (2016)

Colloquium Mathematicae

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Let ℝ be the real line and let Homeo₊(ℝ) be the orientation preserving homeomorphism group of ℝ. Then a subgroup G of Homeo₊(ℝ) is called tightly transitive if there is some point x ∈ X such that the orbit Gx is dense in X and no subgroups H of G with |G:H| = ∞ have this property. In this paper, for each integer n > 1, we determine all the topological conjugation classes of tightly transitive subgroups G of Homeo₊(ℝ) which are isomorphic to ℤⁿ and have countably many nontransitive...