of an edge can be seen as a projective line over ${\bf Z}/p{\bf Z}$, that is the flag variety of ${\rm SL}_2$ over ${\bf Z}/p{\bf Z}$.

### Non-simplicial generalization {#sss - non-simplicial}

We will see, e.g. in \[ss - closed embedding\], that it is often necessary to understand and use reductive algebraic groups over valued fields for [*non-discrete*]{} valuations even if in the initial situation the ground field is discretely valued. The geometric counterpart to this is the necessary use of non-discrete Euclidean buildings. The investigation of such a situation is already covered by the fundamental work by F. Bruhat and J. Tits as written in [@BT1a] and [@BT1b], but the intrinsic definition of a non-discrete Euclidean building is not given there – see [@TitsCome] though, for a reference roughly appearing at the same time as Bruhat-Tits’ latest papers.

The definition of a building in this generalized context is quite similar to the discrete one (\[sss - simplicial\]) in the sense that it replaces an atlas by a collection of “slices” which are still called [*apartments*]{} and turn out to be maximal flat (i.e., Euclidean) subspaces once the building is endowed with a natural distance. What follows can be found 