Lemma 32.4.6. In Situation 32.4.5.

We have $S_{set} = \mathop{\mathrm{lim}}\nolimits _ i S_{i, set}$ where $S_{set}$ indicates the underlying set of the scheme $S$.

We have $S_{top} = \mathop{\mathrm{lim}}\nolimits _ i S_{i, top}$ where $S_{top}$ indicates the underlying topological space of the scheme $S$.

If $s, s' \in S$ and $s'$ is not a specialization of $s$ then for some $i \in I$ the image $s'_ i \in S_ i$ of $s'$ is not a specialization of the image $s_ i \in S_ i$ of $s$.

Add more easy facts on topology of $S$ here. (Requirement: whatever is added should be easy in the affine case.)

## Comments (2)

Comment #1254 by Michael on

Comment #1265 by Johan on