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Journals and Conferences
We prove that various concrete analytic equivalence relations arising in model theory or analysis are complete, i.e. maximum in the Borel reducibility ordering. The proofs use some general results concerning the wider class of analytic quasi-orders.
We study topological properties of conjugacy classes in Polish groups, with emphasis on automorphism groups of homogeneous countable structures. We first consider the existence of dense conjugacy classes (the topological Rokhlin property). We then characterize when an automorphism group admits a comeager conjugacy class (answering a question of Truss) and… (More)
We prove that arbitrary homomorphisms from one of the groups Homeo(2), Homeo(2), Aut(Q, <), Homeo(R) or Homeo(S) into a separable group are automatically continuous. This has consequences for the representations of these groups as discrete groups. For example, it follows, in combination with a result of V. G. Pestov, that any action of the discrete group… (More)
Families of Borel equivalence relations and quasiorders that are cofinal with respect to the Borel reducibility ordering, ≤B , are constructed. There is an analytic ideal on ù generating a complete analytic equivalence relation and any Borel equivalence relation reduces to one generated by a Borel ideal. Several Borel equivalence relations, among them… (More)
A topological group G is defined to have property (OB) if any G-action by isometries on a metric space, which is separately continuous, has bounded orbits. We study this topological analogue of strong uncountable cofinality in the context of Polish groups, where we show it to have several interesting reformulations and consequences. We subsequently apply… (More)
We survey various aspects of the problem of automatic continuity of homomorphisms between Polish groups.
We show that any homomorphism from the homeomorphism group of a compact 2-manifold, with the compact-open topology, or equivalently, with the topology of uniform convergence, into a separable topological group is automatically continuous.
BACKGROUND Successful surgical repair of a regurgitant mitral valve (MV) is dependent on a comprehensive assessment of its complex anatomy. Although there is limited evidence of the feasibility and accuracy of intraoperative real-time 3-dimensional transesophageal echocardiography (RT3DTEE) in MV surgery, its use is increasing worldwide. We designed this… (More)
BACKGROUND The impact of mitral valve surgery on left ventricular outflow tract (LVOT) dimensions is unclear. Real-time three-dimensional transesophageal echocardiography permits excellent visualization of the LVOT and might improve standard two-dimensional measurements. In this study, LVOT area and shape were assessed before and after mitral valve surgery.… (More)