Computable planar curves intersect in a computable point

Issue title: Oberwolfach Workshop on Computability Theory 2018

Guest editors: Vasco Brattka, Rod Downey, Julia F. Knight and Steffen Lempp

Article type: Research Article

Authors: Weihrauch, Klaus^{; *}

Affiliations: Fakultät für Mathematik und Informatik, FernUniversität in Hagen, Universitätsstr. 1, 58084 Hagen, Germany. klaus.weihrauch@fernuni-hagen.de

Correspondence: [*] Corresponding author. klaus.weihrauch@fernuni-hagen.de.

Abstract: Consider two paths f,g:[0;1]→[0;1]2 in the unit square such that f(0)=(0,0), f(1)=(1,1), g(0)=(0,1) and g(1)=(1,0). By continuity of f and g there is a point of intersection. We prove that there is a computable point of intersection if f and g are computable.

Keywords: Computable analysis, planar curves

DOI: 10.3233/COM-180102

Journal: Computability, vol. 8, no. 3-4, pp. 399-415, 2019