In mathematics, Janiszewski's theorem, named after the Polish mathematician Zygmunt Janiszewski, is a result concerning the topology of the plane or extended plane. It states that if A and B are closed subsets of the extended plane with connected intersection, then any two points that can be connected by paths avoiding either A or B can be connected by a path avoiding both of them. The theorem has been used as a tool for proving the Jordan curve theorem[1] and in complex function theory.
Bing, R. H. (1983), The Geometric Topology of 3-Manifolds, Colloquium Publications, vol. 40, American Mathematical Society, ISBN0-8218-1040-5
Pommerenke, C. (1975), Univalent functions, with a chapter on quadratic differentials by Gerd Jensen, Studia Mathematica/Mathematische Lehrbücher, vol. 15, Vandenhoeck & Ruprecht
Pommerenke, C. (1992), Boundary behaviour of conformal maps, Grundlehren der Mathematischen Wissenschaften, vol. 299, Springer, ISBN3540547517
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janiszewski, theorem, mathematics, named, after, polish, mathematician, zygmunt, janiszewski, result, concerning, topology, plane, extended, plane, states, that, closed, subsets, extended, plane, with, connected, intersection, then, points, that, connected, pa. In mathematics Janiszewski s theorem named after the Polish mathematician Zygmunt Janiszewski is a result concerning the topology of the plane or extended plane It states that if A and B are closed subsets of the extended plane with connected intersection then any two points that can be connected by paths avoiding either A or B can be connected by a path avoiding both of them The theorem has been used as a tool for proving the Jordan curve theorem 1 and in complex function theory References edit Proof of the Jordan curve theorem PDF Bing R H 1983 The Geometric Topology of 3 Manifolds Colloquium Publications vol 40 American Mathematical Society ISBN 0 8218 1040 5 Pommerenke C 1975 Univalent functions with a chapter on quadratic differentials by Gerd Jensen Studia Mathematica Mathematische Lehrbucher vol 15 Vandenhoeck amp Ruprecht Pommerenke C 1992 Boundary behaviour of conformal maps Grundlehren der Mathematischen Wissenschaften vol 299 Springer ISBN 3540547517 nbsp This topology related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Janiszewski 27s theorem amp oldid 1133749204, wikipedia, wiki, book, books, library,
