Atlas: Maximal Almost Periodic Groups and a Theorem of Glicksberg by Ta-Sun Wu

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The Eleventh Summer Conference on General Topology and Applications
August 10-13, 1995
University of Southern Maine
Gorham, ME, USA

Organizers
J. Baumgartner, D. Briggs, J. deBakker, B. Flagg, G. Gruenhage, M. Guay, Y. Kong, R. Kopperman, S. Shore, J. Rutten, J. Vaughan

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Maximal Almost Periodic Groups and a Theorem of Glicksberg
by
Ta-Sun Wu
Case Western Reserve University

Let G be a topological group. G is a maximal almost periodic group if there exists a continuous isomorphism from G into a compact group. When G is maximal almost periodic, then there exists a compact group bG and a continuous isomorphism \theta: G --> bG such that for any continuous homomorphism, \phi from G into a compact group H, there exists a (unique) continuous homomorphism \phi^~ : bG --> H such that \phi = \phi^~ o \theta. bG is called the Bohr-compactification of G.

Let G be a maximal almost periodic group and \theta: G --> bG be a Bohr-compactification of G. We say G is a (g) group if for every compact subset D of \theta(G) subset or equal bG, \theta^-1 (D) and D are homeomorphic. We study the structure of locally compact maximal almost periodic groups and the question: when such groups are (g) groups?

Date received: April 12, 1996