Countable Sections for Locally Compact Group Actions. II

Lacunary Sections for Locally Compact Groupoids

It is proved that every second countable locally Hausdorr and locally compact continuous groupoid has a Borel set of units that meets every orbit and is what is called \lacunary," a property that implies that the intersection with every orbit is countable.

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Universal Properties of Group Actions on Locally Compact Spaces

We study universal properties of locally compact G-spaces for countable infinite groups G. In particular we consider open invariant subsets of the G-space βG, and their minimal closed invariant subspaces. These are locally compact free G-spaces, and the latter are also minimal. We examine the properties of these G-spaces with emphasis on their universal properties. As an example of our results,...

Locally Compact, Locally Countable Spaces and Random Reals

In this note I will present a proof that, assuming PFA, if R is a measure algebra then after forcing with R every uncountable locally compact locally countable cometrizable space contains an uncountable discrete set. The lemmas and techniques will be presented in a general form as they may be applicable to other problems.

Equivariant Periodicity for Compact Group Actions

Probably the most basic structural phenomenon of high dimensional topology is Siebenmann’s periodicity theorem [3] (as amended by Nicas [5]), which asserts that the manifolds homotopy equivalent to M are in a one-to-one correspondence with (a subset of, because of nonresolvable honology manifolds [1]) those homotopy equivalent to M×D. The main goal of this paper is to show the following extensi...