  In this paper we consider the "quasidensity" of a subset of the product of a
Banach space and its dual, and give a connection between quasidense sets and
sets of "type (NI)". We discuss "coincidence sets" of certain convex functions
and prove two sum theorems for coincidence sets. We obtain new results on the
Fitzpatrick extension of a closed quasidense monotone multifunction. The
analysis in this paper is self-contained, and independent of previous work on
"Banach SN spaces". This version differs from the previous version because it
is shown that the (well known) equivalence of quasidensity and "type (NI)" for
maximally monotone sets is not true without the monotonicity assumption and
that the appendix has been moved to the end of Section 10, where it rightfully
belongs.
