In mathematics, size theory studies the properties of topological spaces endowed with
History and applications
The beginning of size theory is rooted in the concept of size function, introduced by Frosini. Size functions have been initially used as a mathematical tool for shape comparison in computer vision and pattern recognition.
An extension of the concept of size function to algebraic topology was made in , where size homotopy groups were introduced, together with the natural pseudodistance for
In size theory, size functions and size homotopy groups are seen as tools to compute lower bounds for the natural pseudodistance. Actually, the following link exists between the values taken by the size functions
An analogous result holds for Size homotopy group.
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.