Groups of homeomorphisms and normal subgroups of the group of permutations.

Ramachandran, P.T.

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...