Thanks to both of you

Thanks to Dario Weißmann and Laurent Moret-Bailly
https://stacks.math.columbia.edu/tag/0A11#comment-5941
https://stacks.math.columbia.edu/tag/0A11#comment-5942

spaces-over-fields.tex

@@ -2092,11 +2092,11 @@ \section{Geometrically connected algebraic spaces}
 \end{lemma}
 
 \begin{proof}
-Let $y \in |Y|$ be represented by a morphism $\Spec(K) \to Y$ be a morphism
+Let $y \in |Y|$ be represented by a morphism $\Spec(K) \to Y$
 where $K$ is a field. The fibre of $|X \times_k Y| \to |Y|$ over $y$
-is the image of $|Y_K| \to |X \times_k Y|$ by
+is the image of $|X_K| \to |X \times_k Y|$ by
 Properties of Spaces, Lemma \ref{spaces-properties-lemma-points-cartesian}.
-Thus these fibres are connected by our assumption that $Y$ is
+Thus these fibres are connected by our assumption that $X$ is
 geometrically connected. By
 Morphisms of Spaces, Lemma
 \ref{spaces-morphisms-lemma-space-over-field-universally-open}