jordan curve theorem


jordan curve theorem
noun
Usage: usually capitalized J
: a fundamental theorem of topology: every simple closed curve divides the plane into two regions and is the common boundary between them

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Math.
the theorem that the complement of a simple closed curve can be expressed as the union of two disjoint sets, each having as boundary the given curve. Cf. simple closed curve.
[1915-20; named after M. E. C. JORDAN]

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Jordan curve theorem,
Mathematics. the theorem that a closed curve in a plane divides the plane into an inside and outside region, so that any point in the inside cannot be joined to another point in the outside region without crossing the curve.

Useful english dictionary. 2012.

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