Representing a Differentiable Function as a Cartesian Product

Michael R. Colvin
1983 Proceedings of the American Mathematical Society  
This article produces an elementary proof of a result originally stated without proof by J. Leray. The main result gives conditions so that a continuously differentiable map from a product neighborhood of the origin in R" into R" can be homotoped to a cartesian product of maps on intervals. The resulting product function preserves properties of the original map near the origin.
doi:10.2307/2045509 fatcat:ru6cbhh24vd6njwubeisdsybgu