A second countable locally compact transitive groupoid without open range map

Countable locally 2-arc-transitive bipartite graphs

We present an order-theoretic approach to the study of countably infinite locally 2-arc-transitive bipartite graphs. Our approach is motivated by techniques developed by Warren and others during the study of cycle-free partial orders. We give several new families of previously unknown countably infinite locally-2-arc-transitive graphs, each family containing continuum many members. These exampl...

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.

Relations between positive definite functions and irreducible representations on a locally compact groupoid

If G is a locally compact groupoid with a Haar system λ, then a positive definite function p on G has a form p(x) = 〈L(x)ξ(d(x)), ξ(r(x))〉, where L is a representation of G on a Hilbert bundle H = (G, {Hu}, μ), μ is a quasi invariant measure on G 0 and ξ ∈ L(G,H). [10]. In this paper firt we prove that if μ is a quasi invariant ergodic measure on G, then two corresponding representations of G a...

Locally Unitary Groupoid Crossed Products

We define the notion of a principal S-bundle where S is a groupoid group bundle and show that there is a one-to-one correspondence between principal S-bundles and elements of a sheaf cohomology group associated to S. We also define the notion of a locally unitary action and show that the spectrum of the crossed product is a principal b S-bundle. Furthermore, we prove that the isomorphism class ...

P-Amenable Locally Compact Hypergroups