Along with a suitable definition for neighbourhoods, it is important to be able to identify regions of interest in G. In particular, given a function f : R N → R, it is essential to be able to identify connected subsets of R N for which f is locally maximal. These include pointlike maxima of f (e.g the point x = 0 for f = -|x|), but also spatially-extended maxima (e.g the shell at |x| = 1 of f (x) = -(|x| -1) 2 ). Such a subset (and it's analogue on G) will be refereed to as a maxima family M and the set of maxima families of f as M(f ). Then, for a given family