A Compact Right Group
by
Kenneth Kunen
University of Wisconsin

A right topological group is a topological space X with a group operation · which is right-continuous - that is, for each a in X, the map x --> x·a is continuous.

Assuming CH, there is a compact L-space which is a right group. Note that · cannot also be left-continuous, since then, by Ellis (1957), (X, ·) would be a topological group. As in the standard CH construction, HL is enforced by a measure \mu on X, which in this case is a Haar (right-invariant) measure.

Assuming \diamondsuit, one can get a compact L-space which is both a right group and a Suslin space (that is, the regular open algebra is (\omega, \omega) distributive). Such a space cannot support a measure.

Date received: June 8, 1999