  The electron structure functions are studied in polarized $e^+e^-$
scattering. The formulae for longitudinally and transversely polarized
electrons are presented. The smallnes of the electron mass leads to negligible
cross-sections and asymmetries in some cases. Positivity constraints on the
structure functions and parton densities are constructed and discussed. The
cross-section asymmetries at very high energies, where the inclusion of all
elecroweak bosons is necessary, are calculated. Numerical examples, using the
asymptotic solutions for the parton densities inside the electron, are
presented.
