In his book "Algebraic Geometry and Arithmetic Curves", Liu defines open/closed immersions of locally ringed spaces in terms of topological open/closed immersions:

What does he mean by the terms "topological open (resp. closed) immersion"?

Does he mean that

$f(X)$ is an open (resp. closed) subset of $Y\!,\,$ and

the induced map $X\to f(X); \;x \mapsto f(x)$ is a homeomorphism?

Many thanks! :)