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Group action and shift-compactness

Miller, Harry I. and Ostaszewski, Adam (2012) Group action and shift-compactness. Journal of Mathematical Analysis and Applications, 392 (1). pp. 23-39. ISSN 0022-247X

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Identification Number: 10.1016/j.jmaa.2012.02.021


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.

Item Type: Article
Official URL:
Additional Information: © 2012 The Authors
Divisions: Mathematics
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
Date Deposited: 19 Apr 2012 07:57
Last Modified: 16 May 2024 01:25

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