ntersection of nested closed compact sets is not empty.
Intersection of nested unbounded closed convex sets may be empty. Consider
.
The sets
escape to infinity along the common direction of recession
.
However, if all directions of recession are included in a common linearity
space then this cannot happen as stated in the proposition below.
To see that the
has to be linear consider
and
.
Such
and
fail only the linearity requirement and the conclusion of the theorem.
