In mathematics, an exposed point of a convex set
C
is a point
x
∈
C
at which some continuous linear functional attains its strict maximum over
C
. Such a functional is then said to expose
x
. Note that there can be many exposing functionals for
x
. The set of exposed points of
C
is usually denoted
exp
(
C
)
.
A stronger notion is that of strongly exposed point of
C
which is an exposed point
x
∈
C
such that some exposing functional
f
of
x
attains its strong maximum over
C
at
x
, i.e. for each sequence
(
x
n
)
⊂
C
we have the following implication:
f
(
x
n
)
→
max
f
(
C
)
⟹
∥
x
n
−
x
∥
→
0
. The set of all strongly exposed points of
C
is usually denoted
str
exp
(
C
)
.
There are two weaker notions, that of extreme point and that of support point of
C
.
