No Cover Image

Journal article 42 views 4 downloads

Overt choice / Matthew de Brecht; Arno Pauly; Matthias Schröder

Computability, Pages: 1 - 23

Swansea University Author: Arno, Pauly

Check full text

DOI (Published version): 10.3233/com-190253

Abstract

We introduce and study the notion of overt choice for countably-based spaces and for CoPolish spaces. Overt choice is the task of producing a point in a closed set specified by what open sets intersect it. We show that the question of whether overt choice is continuous for a given space is related t...

Full description

Published in: Computability
ISSN: 2211-3568 2211-3576
Published: IOS Press
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa53986
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract: We introduce and study the notion of overt choice for countably-based spaces and for CoPolish spaces. Overt choice is the task of producing a point in a closed set specified by what open sets intersect it. We show that the question of whether overt choice is continuous for a given space is related to topological completeness notions such as the Choquet-property; and to whether variants of Michael’s selection theorem hold for that space. For spaces where overt choice is discontinuous it is interesting to explore the resulting Weihrauch degrees, which in turn are related to whether or not the space is Fréchet–Urysohn.
Keywords: Weihrauch reducibility, computable topology, quasi-Polish space
Start Page: 1
End Page: 23