4.2 – Aut | Induced chamber structure

Let ${\mathcal{C}}_{\mathbb{L}}$ be a ${\mathcal{P}}_{\mathbb{L}}$-chamber structure.

The collection $${\mathcal{C}}_S=\{\mathcal{D}\cap {\mathcal{P}}_S\mid \mathcal{D}\in {\mathcal{C}}_{\mathbb{L}},\text{Int}(\mathcal{D}\cap {\mathcal{P}}_S)\ne \mathrm{\varnothing }\}$$ is a chamber structure on ${\mathcal{P}}_S$.

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