An affine transformation of the plane under which each point is shifted towards the x-axis, parallel to the y-axis, by a distance proportional to its ordinate. In a Cartesian coordinate system a contraction is given by the relations
$$x'=x,\quad y'=ky,\quad k>0.$$
A contraction of space towards the $xy$-plane, parallel to the $z$-axis, is given by the relations
$$x'=x,\quad y'=y,\quad z'=kz,\quad k>0.$$
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=33091