Let $X$ be a non-discrete Euclidean building. Let $x \in X$, $\Delta\_x$ be the germ of a Weyl-chamber based at $x$ and $\xi$ be a point at infinity. Choose $y \in \Delta\_x$.


Is there an apartment containing $x$, $y$ and $\xi$?


Addendum: is there an apartment containing $x$, $\Delta\_x$ and $\xi$?



Apartment in non-discrete Euclidean building with prescribed properties
See Proposition 1.8 in Parreau's paper on non-discrete Euclidean buildings, which proves several foundational results of this nature.


[https://www-fourier.ujf-grenoble.fr/~parreau/Recherche/Parreau\_1999\_immeubles.pdf](https://www-fourier.ujf-grenoble.fr/%7Eparreau/Recherche/Parreau_1999_immeubles.pdf)


