On a class of homeomorphisms of function spaces preserving the Lindelof number of domains

We consider the class of all homeomorphisms between the function spaces of the form C-p(X), C-p(Y) such that the images of Y and X under their dual and, respectively, inverse dual mappings consist of finitely supported functionals. We prove that if a homeomorphism belongs to this class, then Lindelof numbers l(X) and l(Y) are equal. This result generalizes the known theorem of A. Bouziad for linear homeomorphisms of function spaces.