November 2018
Serhii Bardyla: A topologization of graph inverse semigroups
26/11/18 10:01
Tuesday, November 27, 2018 17:15
Room: D1-215
Speaker: Serhii Bardyla
Title: A topologization of graph inverse semigroups
Abstract. We characterize graph inverse semigroups which admit only discrete locally compact semigroup topology. It will be proved that if a directed graph \(E\) is strongly connected and contains a finite amount of vertices then a locally compact semitopological graph inverse semigroup \(G(E)\) is either compact or discrete. We describe graph inverse semigroups which admit compact semigroup topology and construct a universal object in the class of graph inverse semigroups. Embeddings of graph inverse semigroups into compact-like topological semigroups will be investigated. Also, we discuss some open problems.
Room: D1-215
Speaker: Serhii Bardyla
Title: A topologization of graph inverse semigroups
Abstract. We characterize graph inverse semigroups which admit only discrete locally compact semigroup topology. It will be proved that if a directed graph \(E\) is strongly connected and contains a finite amount of vertices then a locally compact semitopological graph inverse semigroup \(G(E)\) is either compact or discrete. We describe graph inverse semigroups which admit compact semigroup topology and construct a universal object in the class of graph inverse semigroups. Embeddings of graph inverse semigroups into compact-like topological semigroups will be investigated. Also, we discuss some open problems.
Robert Rałowski: Images of Bernstein sets via continuous functions
07/11/18 06:43
Tuesday, November 13, 2018 17:15
Room: D1-215
Speaker: Robert Rałowski
Title: Images of Bernstein sets via continuous functions
Abstract. We examine images of Bernstein sets via continuous mappings. Among other results we prove that there exists a continuous function \(f:\mathbb{R}\to\mathbb{R}\) that maps every Bernstein subset of \(\mathbb{R}\) onto the whole real line. This gives the positive answer to a question of Osipov. This talk is based upon joint paper with Jacek Cichoń and Michał Morayne.
Room: D1-215
Speaker: Robert Rałowski
Title: Images of Bernstein sets via continuous functions
Abstract. We examine images of Bernstein sets via continuous mappings. Among other results we prove that there exists a continuous function \(f:\mathbb{R}\to\mathbb{R}\) that maps every Bernstein subset of \(\mathbb{R}\) onto the whole real line. This gives the positive answer to a question of Osipov. This talk is based upon joint paper with Jacek Cichoń and Michał Morayne.