Let
R
\mathscr {R}
be an
N
I
P
\mathrm {NIP}
expansion of
(
R
,
>
,
+
)
(\mathbb {R},>,+)
by closed subsets of
R
n
\mathbb {R}^n
and continuous functions
f
:
R
m
→
R
n
f : \mathbb {R}^m \to \mathbb {R}^n
. Then
R
\mathscr {R}
is generically locally o-minimal. This follows from a more general theorem on
N
I
P
\mathrm {NIP}
expansions of locally compact groups, which itself follows from a result on quotients of definable sets in
ℵ
1
\aleph _1
-saturated
N
I
P
\mathrm {NIP}
structures by equivalence relations which are both externally definable and
⋀
\bigwedge
-definable. We also show that
R
\mathscr {R}
is strongly dependent if and only if
R
\mathscr {R}
is either o-minimal or
(
R
,
>
,
+
,
α
Z
)
(\mathbb {R},>,+,\alpha \mathbb {Z})
-minimal for some
α
>
0
\alpha > 0
.