Jordan and Schoenflies for non-metric surfaces


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New Zealand Journal of Mathematics

Vol. 40, (2010), Pages 49-58

Alexandre Gabard

Université de Genève

Section de Mathématiques

2-4 rue du Lièvre, CP 64

CH-1211 Genève 4


David Gauld

Department of Mathematics

The University of Auckland

Private Bag 92019


New Zealand

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.

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