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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, size theory studies the properties of topological spaces endowed with {Rk}-valued functions, with respect to the change of these functions. More formally, the subject of size theory is the study of the natural pseudodistance between size pairs. The beginning of size theory is rooted in the concept of size function, introduced in. Size functions have been initially used as a mathematical tool for shape comparison in computer vision and pattern recognition.