Jordan curve

English + theorem Etymology Named after French mathematician Camille Jordan (1838-1922), who first proved the Jordan curve theorem. Noun en topology A non-self-intersecting continuous loop in the plane; a simple closed curve. en 1950 Joseph Leonard Walsh The Location of Critical Points of Analytic and Harmonic Functions w:American Mathematical Society https://books.google.com.au/books?id=X_6VAwAAQBAJ&pg=PA242&dq=%22Jordan+curve%22%7C%22Jordan+curves%22&hl=en&sa=X&ved=0ahUKEwico93GxIrXAhXGVrwKHcHqDYwQ6AEIYzAL#v=onepage&q=%22Jordan%20curve%22%7C%22Jordan%20curves%22&f=false 242 When μ is small and positive, the locus (1) consists of a Jordan curve near each of the Jordan curves belonging to B. en 1992 Konrad Jacobs Invitation to Mathematics https://books.google.com.au/books?id=Mgajuf62voQC&pg=PA164&dq=%22Jordan+curve%22%7C%22Jordan+curves%22&hl=en&sa=X&ved=0ahUKEwico93GxIrXAhXGVrwKHcHqDYwQ6AEIXTAK#v=onepage&q=%22Jordan%20curve%22%7C%22Jordan%20curves%22&f=false 164 If fis a closed curve that is one-one on [0,1] except for f(0) = f(I), then we say that f is a Jordan curve. A Jordan curve can be seen as a homeomorphism from the circle C onto a subset of the given space. en 2001 Constantin Carathéodory Theory of Functions of a Complex Variable 1 https://books.google.com.au/books?id=jyicNQi_6qYC&pg=PA100&dq=%22Jordan+curve%22%7C%22Jordan+curves%22&hl=en&sa=X&ved=0ahUKEwico93GxIrXAhXGVrwKHcHqDYwQ6AEIrwEwGQ#v=onepage&q=%22Jordan%20curve%22%7C%22Jordan%20curves%22&f=false 100 The most general Jordan curves, like the triangle, have the property of dividing the plane into two regions. Synonyms non-self-intersecting loop in the plane en simple closed curve Related terms en Jordan arc Further reading Denjoy–Riesz theorem Osgood curve en Curves en eponyms