Sections of Serre fibrations with 2-manifold fibers

It was proved by H. Whitney in 1933 that a Serre fibration of compact metric spaces admits a global section provided every fiber is homeomorphic to the unit interval [ 0 , 1 ] . Results of this paper extend Whitneyʹs theorem to the case when all fibers are homeomorphic to a given compact two-dimensional manifold.