In mathematics, size theory studies the properties of topological spaces endowed with
A survey of size theory can be found in .
[2] Size functions have been initially used as a mathematical tool for shape comparison in computer vision and pattern recognition.
[3][4][5][6][7][8][9][10] An extension of the concept of size function to algebraic topology was made in the 1999 Frosini and Mulazzani paper [11] where size homotopy groups were introduced, together with the natural pseudodistance for
An extension to homology theory (the size functor) was introduced in 2001.
[12] The size homotopy group and the size functor are strictly related to the concept of persistent homology group [13] studied in persistent homology.
It is worth to point out that the size function is the rank of the
Actually, the following link exists between the values taken by the size functions
,[14][15] An analogous result holds for size homotopy group.
[11] The attempt to generalize size theory and the concept of natural pseudodistance to norms that are different from the supremum norm has led to the study of other reparametrization invariant norms.