Group action and shift-compactness

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:392

Article

Miller, Harry I.²  Ostaszewski, A. J.¹ 

[1] London Sch Econ, Dept Math, London WC2A 2AE, England

[2] Int Univ Sarajevo, Dept Math, Sarajevo, Bosnia & Herceg

关键词: Shift-compactness;    Almost completeness;    alpha-Favourability;    Effros Open Mapping Theorem;    Analytic sets;    Non-commutative groups;    Group-norm;    Topological groups;    Van Mill separation property;    Density topology;    Hit-and-miss topologies;    Fox-Mosco convergence;    Ideal topologies;   

DOI  :  10.1016/j.jmaa.2012.02.021

来源: Elsevier

【 摘 要 】

Shift-compactness has recently been found to be the foundation stone of classical, as well as topological, regular variation; most recently it has come again to prominence in new proofs of the Effros Open Mapping Principle of group action, another ingredient of topological regular variation. Using the real line under the Euclidean and density topologies as a paradigm, we develop group-action versions of shift-compactness theorems for Baire groups acting on Baire spaces under metrizable topologies and under certain refinements of these. One aim is to pursue constructive approaches rather than rely on plain Baire-category methods (so keeping more to the Banach-Mazur strategic approach). Along the way we uncover three new coarse topologies for groups of homeomorphisms. A second purpose is to establish limitations of the shift-compactness methodology. (C) 2012 Published by Elsevier Inc.

【 授权许可】

Free