An affine transformation of the plane under which each point is shifted towards the -axis, parallel to the -axis, by a distance proportional to its ordinate. In a Cartesian coordinate system a contraction is given by the relations
A contraction of space towards the -plane, parallel to the -axis, is given by the relations
More usually, a contraction is defined as a transformation of a metric space that reduces distances. The notion defined above has no established name in Western literature, but is sometimes called a compression or compression-expansion.
Contraction(2). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Contraction(2)&oldid=15206