Let $\phi:A\to B$ be an epimorphism in the category of commutative rings, we can find that the induced continuous map $\phi^*$ from Spec$B$ to Spec$A$ is injective as a map between sets,
I want to know if $\phi^*$ is also an immersion of topological spaces, that is if Spec$B$ is homeomorphic to $\phi^*(\mathrm{Spec}(B))$ under the map $\phi^*$ ?
Taking localization and quotient are the just the special cases of epimorphisms, how far are they away from epimorphisms?
Is there an explicit construction of epimorphisms in CRings ?
Thanks..