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SUMMARY:Mathieu Hoyrup (LORIA)
DTSTART:20210202T150000Z
DTEND:20210202T160000Z
DTSTAMP:20260423T021726Z
UID:CTA/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CTA/49/">The
  fixed-point property for represented spaces</a>\nby Mathieu Hoyrup (LORIA
 ) as part of Computability theory and applications\n\n\nAbstract\nErshov's
  generalization of Kleene's recursion theorem is a fixed-point theorem for
  computable multi-valued functions on numbered sets. We study its continuo
 us version for continuous multi-valued functions on represented spaces. We
  obtain results explaining why the fixed-point theorem usually holds unifo
 rmly and why in most cases it can only be proved by the diagonal argument.
  We investigate restricted classes of spaces\, for which we give a complet
 e characterization of the spaces with the fixed-point property: the counta
 bly-based spaces and the spaces of open sets. We also give an application 
 to the base-complexity classification of topological spaces.\n
LOCATION:https://researchseminars.org/talk/CTA/49/
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