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The Fréchet Distance is a metric function upon an infinite ] of ] <X<sub>1</sub>,d<sub>1</sub>>,<X<sub>2</sub>,d<sub>2</sub>>..., defined by: The Fréchet metric is a metric function upon an infinite ] of ] <X<sub>1</sub>,d<sub>1</sub>>,<X<sub>2</sub>,d<sub>2</sub>>..., defined by:
<math>d(x,y)=\sum\frac{1}{2^n}\frac{d_{n}(x_{n},y_{n})}{1+d_{n}(x_{n},y_{n})}</math> <math>d(x,y)=\sum\frac{1}{2^n}\frac{d_{n}(x_{n},y_{n})}{1+d_{n}(x_{n},y_{n})}</math>


Revision as of 16:08, 13 December 2006

Maurice Fréchet (September 2, 1878 – June 4, 1973) was a French mathematician.

In 1906, he introduced the concept of metric space, and was one of the founders of functional analysis. He also coined the term compact space. He was a student of Jacques Hadamard at École Normale Supérieure.


The Fréchet metric is a metric function upon an infinite cartesian product of metric spaces <X1,d1>,<X2,d2>..., defined by: d ( x , y ) = ∑ 1 2 n d n ( x n , y n ) 1 + d n ( x n , y n ) {\displaystyle d(x,y)=\sum {\frac {1}{2^{n}}}{\frac {d_{n}(x_{n},y_{n})}{1+d_{n}(x_{n},y_{n})}}}

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