My question concerns the statement that open immersions are stable under base change. Therefore for open immersion $f:X \to S$ the base change $g:X \times _S Y \to Y$ is also an open immersion.
In https://stacks.math.columbia.edu/tag/01JU is explained that it follows from following lemma:
https://stacks.math.columbia.edu/tag/01JR
Can anybody explain how the statement above is concluded from this lemma. I dont see it.
The lemma states that if you have two $S$-schemes $X'$ and $Y',$ and open subschemes $U\subseteq S,$ $V\subseteq X',$ and $W\subseteq Y',$ the canonical map $$V\times_U W\to X'\times_S Y'$$ is an open immersion.
To obtain your statement from this lemma, Set $X' = U = S,$ $V = X,$ and $W = Y' = Y.$ Then the open immersion in the lemma becomes $$V\times_U W = X\times_S Y\to X'\times_S Y' = S\times_S Y = Y,$$ which is what you wanted to show was an open immersion.