View source for Contraction(2)

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

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A contraction of space towards the <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025820/c0258204.png" />-plane, parallel to the <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025820/c0258205.png" />-axis, is given by the relations

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====Comments====
More usually, a contraction is defined as a [[Transformation|transformation]] of a [[Metric space|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.