Lemma 26.3.5. Let $f : X \to Y$ be a morphism of locally ringed spaces. Let $U \subset X$, and $V \subset Y$ be open subsets. Suppose that $f(U) \subset V$. There exists a unique morphism of locally ringed spaces $f|_ U : U \to V$ such that the following diagram is a commutative square of locally ringed spaces

$\xymatrix{ U \ar[d]_{f|_ U} \ar[r] & X \ar[d]^ f \\ V \ar[r] & Y }$

Proof. Omitted. $\square$

There are also:

• 2 comment(s) on Section 26.3: Open immersions of locally ringed spaces

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).