  In this article, after recalling and discussing the conventional extremality,
local extremality, stationarity and approximate stationarity properties of
collections of sets and the corresponding (extended) extremal principle, we
focus on extensions of these properties and the corresponding dual conditions
with the goal to refine the main arguments used in this type of results,
clarify the relationships between different extensions and expand the
applicability of the generalised separability results. We introduce and study
new more universal concepts of relative extremality and stationarity and
formulate the relative extended extremal principle. Among other things, certain
stability of the relative approximate stationarity is proved. Some links are
established between the relative extremality and stationarity properties of
collections of sets and (the absence of) certain regularity, lower
semicontinuity and Lipschitz-like properties of set-valued mappings.
