Displaying similar documents to “Non-locally compact Polish groups and two-sided translates of open sets”

Equivalence relations induced by some locally compact groups of homeomorphisms of 2 ℕ

B. Majcher-Iwanow (2005)

Colloquium Mathematicae

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Let T be a locally finite rooted tree and B(T) be the boundary space of T. We study locally compact subgroups of the group TH(B(T)) = ⟨Iso(T),V⟩ generated by the group Iso(T) of all isometries of B(T) and the group V of Richard Thompson. We describe orbit equivalence relations arising from actions of these groups on B(T).

Automorphism groups of right-angled buildings: simplicity and local splittings

Pierre-Emmanuel Caprace (2014)

Fundamenta Mathematicae

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We show that the group of type-preserving automorphisms of any irreducible semiregular thick right-angled building is abstractly simple. When the building is locally finite, this gives a large family of compactly generated abstractly simple locally compact groups. Specialising to appropriate cases, we obtain examples of such simple groups that are locally indecomposable, but have locally normal subgroups decomposing non-trivially as direct products, all of whose factors are locally normal. ...

Haar null and non-dominating sets

Sławomir Solecki (2001)

Fundamenta Mathematicae

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We study the σ-ideal of Haar null sets on Polish groups. It is shown that on a non-locally compact Polish group with an invariant metric this σ-ideal is closely related, in a precise sense, to the σ-ideal of non-dominating subsets of ω ω . Among other consequences, this result implies that the family of closed Haar null sets on a Polish group with an invariant metric is Borel in the Effros Borel structure if, and only if, the group is locally compact. This answers a question of Kechris....

Sets of p-multiplicity in locally compact groups

I. G. Todorov, L. Turowska (2015)

Studia Mathematica

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We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if E * = ( s , t ) : t s - 1 ∈ E is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone-von Neumann Theorem.

Covering locally compact groups by less than 2 ω many translates of a compact nullset

Márton Elekes, Árpád Tóth (2007)

Fundamenta Mathematicae

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Gruenhage asked if it was possible to cover the real line by less than continuum many translates of a compact nullset. Under the Continuum Hypothesis the answer is obviously negative. Elekes and Stepr mans gave an affirmative answer by showing that if C E K is the well known compact nullset considered first by Erdős and Kakutani then ℝ can be covered by cof() many translates of C E K . As this set has no analogue in more general groups, it was asked by Elekes and Stepr mans whether such a result...

Notes on locally internal uninorm on bounded lattices

Gül Deniz Çaylı, Ümit Ertuğrul, Tuncay Köroğlu, Funda Karaçal (2017)

Kybernetika

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In the study, we introduce the definition of a locally internal uninorm on an arbitrary bounded lattice L . We examine some properties of an idempotent and locally internal uninorm on an arbitrary bounded latice L , and investigate relationship between these operators. Moreover, some illustrative examples are added to show the connection between idempotent and locally internal uninorm.

On zero-dimensionality of subgroups of locally compact groups

Dmitriĭ B. Shakhmatov (1991)

Commentationes Mathematicae Universitatis Carolinae

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Improving the recent result of the author we show that ind H = 0 is equivalent to dim H = 0 for every subgroup H of a Hausdorff locally compact group G .