The fixed-point property for represented spaces

Mathieu Hoyrup (LORIA)

02-Feb-2021, 15:00-16:00 (3 years ago)

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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