  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.
