On Glimm's Theorem for almost Hausdorff G-spaces

Abstract

We establish a characterization of the well-behaved orbits of a totally Baire $G$-space of a hereditary Lindelöf locally compact group under a mild assumption of Hausdorffness. Furthermore we give a reformulation of the proof of Glimm's theorem generalizing the assertion from second countable to hereditary Lindelöf locally compact groups acting on second countable spaces.

arXiv commentExtensive revision. Correction of an error in the proof of Theorem 12 of the first version