6 papers
Width bounds and Steinhaus property for unit groups of continuous rings
Josefin Bernard, Friedrich Martin Schneider
We prove an algebraic decomposition theorem for the unit group of an arbitrary non-discrete irreducible, continuous ring (in von Neumann's sense), which entail…
Unitary representations and von Neumann's continuous geometries
Friedrich Martin Schneider, Andreas Thom
We prove that the unit group of a non-discrete irreducible, continuous ring, in the sense of John von Neumann, does not admit any non-trivial unitary representation continuous with…
Projective simplicity and Bergman's property for unit groups of continuous rings
Friedrich Martin Schneider
We prove that the projective unit group , i.e., the quotient of the unit group modulo its center, of any non-discrete irreducible, continuous ring…
Geometric properties of unit groups of von Neumann's continuous rings
Friedrich Martin Schneider
We prove that, if is a non-discrete irreducible, continuous ring, then its unit group , equipped with the topology generated by the rank metric, is topologicall…
Groups without unitary representations, submeasures, and the escape property
Friedrich Martin Schneider, SÅawomir Solecki
We give new examples of topological groups that do not have non-trivial continuous unitary representations, the so-called exotic groups. We prove that all groups of the form $L^0(Ï…
Echeloned Spaces
Maxime Gheysens, Bojana Pavlica, Christian Pech +2
We introduce the notion of echeloned spaces - an order-theoretic abstraction of metric spaces. The first step is to characterize metrizable echeloned spaces. It turns out that morp…