Jordan and Schoenflies for non-metric surfaces
New Zealand Journal of Mathematics
Vol. 40, (2010), Pages 49-58
Université de Genève
Section de Mathématiques
2-4 rue du Lièvre, CP 64
CH-1211 Genève 4
Department of Mathematics
The University of Auckland
Private Bag 92019
Abstract We show that both the Jordan curve theorem and the Schoenflies theorem extend to non-metric manifolds (at least in the two-dimensional context), and conclude with some dynamical applications à la Poincaré-Bendixson.
Keywords Non-metric manifolds, Jordan curve theorem, Schoenflies theorem.
Classification (MSC2000) Primary: 57N05; Secondary: 57N35, 57N50.