The Solecki dichotomy for functions with analytic graphs

A dichotomy discovered by Solecki says that a Baire class 1 function from a Souslin space into a Polish space either can be decomposed into countably many continuous functions, or else contains one particular function which cannot be so decomposed. In this paper we generalize this dichotomy to arbitrary functions with analytic graphs. We provide a "classical" proof, which uses only elementary combinatorics and topology.