For an additive
κ
\kappa
-metric space
X
X
with an
s
(
x
)
s\left ( x \right )
-continuous
κ
\kappa
-metric
d
(
x
,
C
)
d\left ( {x,C} \right )
, we prove that
X
X
is metrizable, and that if
d
(
x
,
C
)
d\left ( {x,C} \right )
is locally regular, then
z
(
x
,
y
)
z\left ( {x,y} \right )
is bicontinuous, and
ρ
(
x
,
y
)
=
z
(
x
,
y
)
+
z
(
x
,
y
)
\rho \left ( {x,y} \right ) = z\left ( {x,y} \right ) + z\left ( {x,y} \right )
is a metric on
X
X
which agrees with the topology of
X
X
.