Let $\rho:X^{\text{an}}\longrightarrow B$ be a continuous map to a topological space $B$. For any point $b\in B$, we say that $\rho$ is an affinoid torus fibration at $b$ if there exists an open neighbourhood $U$ of $b$ in $B$, such that the restriction to $\rho^{-1}(U)$ fits into a commutative diagram:

$V$ being an open subset of $\mathbb{R}^{n}$, the upper horizontal map an isomorphism of analytic spaces, the lower horizontal map a homeomorphism, and the map $\val$ defined as in Section 1.5.