Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 4

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

The automorphism group of the Lebesgue measure has no non-trivial subgroups of index $< 2^{ω}$

100%
Malicki M.
Colloquium Mathematicum
|
2013
|
tom 133
|
nr 2
169-174
EN
We show that the automorphism group Aut([0,1],λ) of the Lebesgue measure has no non-trivial subgroups of index $< 2^{ω}$.
2
Content available remote

Non-locally compact Polish groups and two-sided translates of open sets

100%
Malicki M.
Fundamenta Mathematicae
|
2008
|
tom 200
|
nr 3
279-295
EN
This paper is devoted to the following question. Suppose that a Polish group G has the property that some non-empty open subset U is covered by finitely many two-sided translates of every other non-empty open subset of G. Is then G necessarily locally compact? Polish groups which do not have the above property are called strongly non-locally compact. We characterize strongly non-locally compact Polish subgroups of $S_{∞}$ in terms of group actions, and prove that certain natural classes of non-locally compact Polish groups are strongly non-locally compact. Next, we discuss applications of these results to the theory of left Haar null sets. Finally, we show that Polish groups such as the isometry group of the Urysohn space and the unitary group of the separable Hilbert space are strongly non-locally compact.
3
Content available remote

The automorphism group of the random lattice is not amenable

100%
Malicki M.
Fundamenta Mathematicae
|
2014
|
tom 226
|
nr 3
245-252
EN
We prove that the automorphism group of the random lattice is not amenable, and we identify the universal minimal flow for the automorphism group of the random distributive lattice.
4
Content available remote

Abelian pro-countable groups and orbit equivalence relations

100%
Malicki M.
Fundamenta Mathematicae
|
2016
|
tom 233
|
nr 1
83-99
EN
We study a class of abelian groups that can be defined as Polish pro-countable groups, as non-archimedean groups with a compatible two-sided invariant metric or as quasi-countable groups, i.e., closed subdirect products of countable discrete groups, endowed with the product topology. We show that for every non-locally compact, abelian quasi-countable group G there exists a closed L ≤ G and a closed, non-locally compact K ≤ G/L which is a direct product of discrete countable groups. As an application we prove that for every abelian Polish group G of the form H/L, where H,L ≤ Iso(X) and X is a locally compact separable metric space (in particular, for every abelian, quasi-countable group G), the following holds: G is locally compact iff every continuous action of G on a Polish space Y induces an orbit equivalence relation that is reducible to an equivalence relation with countable classes.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.