  Maximally monotone operators play important roles in optimization,
variational analysis and differential equations. Finding zeros of maximally
monotone operators has been a central topic. In a Hilbert space, we show that
most resolvents are super-regular, that most maximally monotone operators have
a unique zero and that the set of strongly monotone mapping is of first
category although each strongly monotone operator has a unique zero. The
results are established by applying the Baire Category Theorem to the space of
nonexpansive mappings.
