A metric form of microtransitivity

Hohti, Aarno

doi:10.1090/s0002-9939-1986-0835893-x

Cited by 2 publications

(2 citation statements)

References 14 publications

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“…A. Hohti and H. Junnila [17] showed that every homogeneous locally compact separable metrizable space X is Lipschitz homogeneous. In the compact case, Hohti [16,Theorem 3.1] strengthened this result by showing that a homogeneous compact metrizable space X admits a metric ρ such that X is a coset space of L(X, ρ) in the compact-open topology.…”

Section: Theorem 11 ([30])mentioning

confidence: 99%

Coset spaces of metrizable groups

Antonyan

Kozlov

2022

Colloq. Math.

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We characterize topological spaces which are coset spaces of (separable) metrizable groups and complete metrizable (Polish) groups. Moreover, it is shown that for a G-space X with a d-open action there is a topological group H of weight and cardinality less than or equal to the weight of X such that H admits a d-open action on X. This is further applied to show that if X is a separable metrizable coset space of some topological group, then X has a Polish extension which is a coset space of a Polish group.

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Section: Theorem 11 ([30])mentioning

confidence: 99%

Coset spaces of metrizable groups

Antonyan

Kozlov

2022

Colloq. Math.

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show abstract

“…A. Hohti and H. Junnila [16] showed that every homogeneous locally compact separable metrizable space X is Lipschitz homogeneous. A. Hohti [15,Theorem 3.1] strengthened this result in a compact case showing that a compact metrizable X is a coset space of L(X, ρ) in the compact open topology for some metric ρ on X.…”

Section: Introductionmentioning

confidence: 95%

Coset spaces of metrizable groups

Antonyan¹,

Antonyan²,

Козлов³

2017

Preprint

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We characterize coset spaces of topological groups which are coset spaces of (separable) metrizable groups and complete metrizable (Polish) groups. Besides, it is shown that for a G-space X with a d-open action there is a topological group H of weight and cardinality less than or equal to the weight of X such that H admits a d-open action on X. This is further applied to show that if X is a separable metrizable coset space then X has a Polish extension which is a coset space of a Polish group.

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A metric form of microtransitivity

Abstract: Abstract.We prove that every homogeneous compact metrizable space X has a compatible metric for which X is Lipschitz homogeneous and for which the group L( X) of Lipschitz homeomorphisms of X acts Lipschitz microtransitively on X.

Cited by 2 publications

References 14 publications

Coset spaces of metrizable groups

Coset spaces of metrizable groups

Coset spaces of metrizable groups

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