A point
x
∈
X
x \in X
is inner if there exists an open set
U
U
containing
x
x
such that for each open set
V
V
with
x
∈
V
⊆
U
x \in V \subseteq U
, the inclusion homomorphism
i
∗
:
{i^* }:
:
H
∗
(
X
,
X
∖
V
)
→
H
∗
(
X
,
X
∖
U
)
{H^*}(X,X \setminus V) \to {H^*}(X,X \setminus U)
is nontrivial. In this note it is proved that, if
X
X
is a compact, chainwise connected topological semilattice of codimension
n
n
, and
x
x
is a point of breadth
n
+
1
n + 1
, then
x
x
is an inner point.