  We study the space of loops into a hypersurface complement, and show that the
corresponding topological algebra of Laurent series with coefficients in
$\mathcal{O}(L\mathbf{A}^{d}_{f})$ is a topological localisation of
$\mathcal{O}(L\mathbf{A}^{d})$. This requires introducing a small amount of
non-Archimedean functional analysis. In particular we work with topological
algebras whose topology is generated by a family of sub-multiplicative,
non-Archimedean semi-norms.
