2009/08/11 by Janusz Pawlikowski, Pawlikowski, Janusz, Marcin Sabok +1
Mathematics · #03E15 #26A15 #54H05 #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #math.GN #math.LO #msc:03E15 #msc:26A15 #msc:54H05
paper · pdf · doi:10.48550/arxiv.0908.1544
arxiv created 2009/08/11 · arxiv updated 2009/12/01
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.