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

• Autorzy: Maciej Malicki
• Języki publikacji: EN

Abstrakty

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.

Kategorie tematyczne

• 28C10: Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
• 54E50: Complete metric spaces
• 54H15: Transformation groups and semigroups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 200
• Numer: 3
• Strony: 279-295

Daty

wydano

2008

Twórcy

autor

Maciej Malicki

• Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green St., Urbana, IL 61801, U.S.A.
• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/fm200-3-3