13 May 2008

2:30 - 4:00 M Barr

Z-compact topological abelian groups

Abstract:
Topologists have studied the concept of E-compact spaces.  Generally,
E is a hausdorff space and a space X is E-compact if it is a closed
subspace of a power of E.  In the three cases that have been most
studied, where E is the unit interval, the real line, or the natural
numbers, it turns out that E-compact can be characterized as spaces
that are equalizers of two maps between powers of E.  When is not
hausdorff, the latter makes more sense.  In fact sober spaces can be
characterized as those which are equalizers of two maps between powers of the
Sierpinski space.

All this leads to our definition of the title.  An abelian group is
Z-compact if it is a kernel of a map (equivalently equalizer of two
maps) between powers of Z.  This talk will describe some of the
properties of Z-compact groups.  For example, they can be
characterized as the fixed groups for the double-dual-into-Z functor.