The Jordan Curve Theorem Is Nontrivial

The classical Jordan curve theorem (JCT) says, Every Jordan curve (a non-self-intersecting continuous loop in the plane) separates the plane into exactly two components. It is often mentioned just in passing in courses ranging from liberal arts mathematics courses, where it is an illuminating exampl...

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Bibliographic Details
Published inThe Best Writing on Mathematics 2013 Vol. 4; pp. 120 - 129
Main Authors Ross, Fiona, Ross, William T
Format Book Chapter
LanguageEnglish
Published United States Princeton University Press 19.01.2014
Subjects
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Arts
Behavioral sciences
Complex analysis
Curves
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Educators
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Euclidean geometry
Games
Geometric planes
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Geometry
Health sciences
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Logic
Logical theorems
Mathematical analysis
Mathematical expressions
Mathematical theorems
MATHEMATICS
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Plane geometry
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Summary:The classical Jordan curve theorem (JCT) says, Every Jordan curve (a non-self-intersecting continuous loop in the plane) separates the plane into exactly two components. It is often mentioned just in passing in courses ranging from liberal arts mathematics courses, where it is an illuminating example of an “obvious” statement that is difficult to prove, to undergraduate and graduate topology and complex analysis, where it tends to break the flow. In complex analysis, it is especially given short shrift. There are several reasons for this short shrift. For one, a professor has bigger fish to fry. There are the theorems of
ISBN:9780691160412
0691160414
DOI:10.1515/9781400847990-014