The fixed-point property for represented spaces
Mathieu Hoyrup (LORIA)
Abstract: Ershov's generalization of Kleene's recursion theorem is a fixed-point theorem for computable multi-valued functions on numbered sets. We study its continuous version for continuous multi-valued functions on represented spaces. We obtain results explaining why the fixed-point theorem usually holds uniformly 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 complete characterization of the spaces with the fixed-point property: the countably-based spaces and the spaces of open sets. We also give an application to the base-complexity classification of topological spaces.
logic
Audience: researchers in the topic
Computability theory and applications
Series comments: Description: Computability theory, logic
The goal of this endeavor is to run a seminar on the platform Zoom on a weekly basis, perhaps with alternating time slots each of which covers at least three out of four of Europe, North America, Asia, and New Zealand/Australia. While the meetings are always scheduled for Tuesdays, the timezone varies, so please refer to the calendar on the website for details about individual seminars.
Organizers: | Damir Dzhafarov*, Vasco Brattka*, Ekaterina Fokina*, Ludovic Patey*, Takayuki Kihara, Noam Greenberg, Arno Pauly, Linda Brown Westrick |
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