Jordan curve theorem

English Noun en noun Jordan curve theorem en topology The theorem that states that a simple closed curve (Jordan curve) divides the plane into precisely two distinct areas. en 1995 William Fulton Algebraic Topology: A First Course https://books.google.com.au/books?id=8-OPBAAAQBAJ&pg=PA343&dq=%22Jordan+curve+theorem%22%7C%22Jordan+curve+theorems%22&hl=en&sa=X&ved=0ahUKEwjh_umkvYvXAhWElJQKHZ8CBKsQ6AEIpwEwFw#v=onepage&q=%22Jordan%20curve%20theorem%22%7C%22Jordan%20curve%20theorems%22&f=false 343 Springer There is a vast generalization of the Jordan curve theorem to higher dimensions. en 2001 Theodore Gamelin Complex Analysis https://books.google.com.au/books?id=61BO2UY9QN4C&pg=PA249&dq=%22Jordan+curve+theorem%22%7C%22Jordan+curve+theorems%22&hl=en&sa=X&ved=0ahUKEwjh_umkvYvXAhWElJQKHZ8CBKsQ6AEIRTAH#v=onepage&q=%22Jordan%20curve%20theorem%22%7C%22Jordan%20curve%20theorems%22&f=false 249 Springer The Jordan curve theorem asserts that a simple closed curve in the complex plane divides the plane into exactly two connected components, one bounded (the "inside") and the other unbounded (the "outside" ). en 2004 Nelson G. Markley Principles of Differential Equations https://books.google.com.au/books?id=MWh8Xu6Cl6YC&pg=PA193&dq=%22Jordan+curve+theorem%22%7C%22Jordan+curve+theorems%22&hl=en&sa=X&ved=0ahUKEwjh_umkvYvXAhWElJQKHZ8CBKsQ6AEIazAN#v=onepage&q=%22Jordan%20curve%20theorem%22%7C%22Jordan%20curve%20theorems%22&f=false 193 Wiley The principal reason that orbit behavior in the plane is more limited than in higher dimensions is the Jordan curve theorem. Local sections will be the primary tool used to exploit the Jordan curve theorem. en Jordan curve theorem 2009, Josef Šlapal, Jordan Curve Theorems with Respect to Certain Pretopologies on , Srecko Brlek, Christophe Reutenauer, Xavier Provençal (editors), Discrete Geometry for Computer Imagery: 15th IAPR International Conference, Springer, LNCS 5810, page 252, Some known Jordan curves in the basic topology are used to prove Jordan curve theorems that identify Jordan curves among simple closed ones in each of the four quotient pretopologies. en Curves en eponyms