  In this work, we provide some novel results that establish both the existence
of Henig global proper efficient points and their density in the efficient set
for vector optimization problems in arbitrary normed spaces. Our results do not
require the assumption of convexity, and in certain cases, can be applied to
unbounded sets. However, it is important to note that a weak compactness
condition on the set (or on a section of it) and a separation property between
the order cone and its conical neighborhoods remains necessary. The weak
compactness condition ensures that certain convergence properties hold. The
separation property enables the interpolation of a family of Bishop-Phelps
cones between the order cone and each of its conic neighborhoods. This
interpolation, combined with the proper handling of two distinct types of conic
neighborhoods, plays a crucial role in the proofs of our results, which include
as a particular case other results that have already been established under
more restrictive conditions.
