Teoremi di normalizzazione per l'omotopia regolare dei grafi

Given a metric compact spaceS and a finite graphG we show that:

a)	each regular function ofS inG is regularly homotopic to a strongly regular function;
b)	each regular function ofS inG is regularly homotopic to an almost constant function in respect of an appropriate partition ofS.

Hence it follows that in each class of regularn-dimensional homotopy ofG can always be chosen as representative an almost constant path in respect of a suitable triangulation ofn-cubeI ⁿ.