  The basic results for nonlinear operators are given. These results include
nonlinear versions of classical uniform boundedness theorem and Hahn-Banach
theorem. Furthermore, the mappings from a metrizable space into another normed
space can fall in some normed spaces by defining suitable norms. The results
for the mappings on the metrizable spaces can be applied to the operators on
the space of bounded linear functionals corresponding to the Dirac's delta
function.
