Všechny tři přednášky se budou konat v seminární místnosti Ústavu matematiky E/309 v budově na Kolejní 4.

• 20.5. proběhne přednáška s názvem Decimal Approximation. Abstract: The usual decimal approximation of the reals
  represents them as a categorical limit of finite neighborhood spaces and special continuous maps.
• 23.5. proběhne přednáška s názvem Generalizing distance. Abstract: Most of us first learn to deal with limits and
  continuity in calculus, where "epsilon-delta" proofs, using the idea of distance between real numbers d(x,y)=|x-y|, and
  that of positive number, are the key tools. Many structures (e.g. topologies, uniformities) have been defined to handle
  these and related ideas more generally. We discuss natural ways to generalize these so-called "metric" (= distance)
  ideas and show that these other spaces and their ideas of limit always arise from the generalized distances.
• 24.5. proběhne přednáška s názvem Asymmetric topological groups and semigroups. Abstract: The additive reals, with the topology U of upper open intervals, are a group with T0 topology, with respect to which + is continuous. E, the usual Euclidean topology can be recovered from U and the usual order on the reals is the specialization order of U. Thus U tells
  more than does E. In this talk we discuss semigroups with T0 topologies, and in particular we extend Ellis' theorem, and the fact that each compact T2 cancellative semigroup is a topological group, to non-T1 cases. We also discuss the existence of a collection of subinvariant quasimetrics that give rise to these topologies.

Všichni zájemci, i z řad studentů, jsou na přednášky srdečně zváni.

J.Šlapal