  Using the closure operator that defines a subtractive ideal of a semiring
$S$, in this note we introduce a topology on the set of all ideals of $S$
induced by that operator. We show that the corresponding subtractive space is
$T_0$ and every nonempty irreducible closed set has a unique generic point,
whereas the restricted subspace of subtractive ideals is $T_1$. Using a
semiring homomorphism, we obtain a continuous map between the corresponding
subtractive spaces.
