any (images of) Weyl chambers, there is an apartment of $X$ containing sub-Weyl chambers of each.

-   Given any apartment $\mathbb{A}$ and any point $x \in \mathbb{A}$, there is a $1$-lipschitz retraction map $r = r_{x,\mathbb{A}} : \mathcal{B} \to \mathbb{A}$ such that $r \mid_\mathbb{A} = {\rm id}_\mathbb{A}$ and $r^{-1}(x) = \{x \}$.

The above definition is taken from [@Parreau II.1.2]; in these axioms a [*Weyl chamber*]{} is the affine counterpart to the previously defined notion of a [*Weyl chamber*]{} and a “sub-Weyl chamber” is a translate of the initial Weyl chamber which is completely contained in the latter.

A different set of axioms is given in G. Rousseau’s paper [@RousseauGrenoble §6]. It is interesting because it provides a unified approach to simplicial and non-simplicial buildings via incidence requirements on apartments. The possibility to obtain a non-discrete building with Rousseau’s axioms is contained in the model for an apartment and the definition of a facet as a filter. The latter axioms are adapted to some algebraic situations which cover the case of Bruhat-Tits theory over non-complete valued fields – see [@RousseauGrenoble Remark 9.4] for more details and comparisons.

In this paper we do not use the plain word “chamber” though it 