Proposition 8.4.
Assuming that:
(
F
,
|
∙
|
)
is a complete
discretely valued field
f
(
X
)
=
∑
i
=
0
n
a
i
X
i
∈
O
K
[
X
]
a separable irreducible monic polynomial
α
∈
K
sep
a root of
f
Then
there exists
𝜀
>
0
such that for any
g
(
X
)
=
∑
i
=
0
n
b
i
X
i
∈
O
K
[
X
]
monic with
|
a
i
−
b
i
|
<
𝜀
for all
i
, there exists a root
β
of
g
(
X
)
such that
K
(
α
)
=
K
(
β
)
.