ScalingStacks

Lemma 2.2 . [0157]

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Lemma 2.2.

There exists a family ((𝒱α,zα))α∈A(({\mathcal{V}}_{\alpha},z_{\alpha}))_{\alpha\in A} of adapted coordinate charts, such that (𝒱α)α({\mathcal{V}}_{\alpha})_{\alpha} forms a locally finite covering of DD and such that the strata YαY_{\alpha} of the 𝒱α{\mathcal{V}}_{\alpha} satisfy

⋂β∈B𝒱β≠∅⟹⋂β∈BYβ≠∅\bigcap_{\beta\in B}{\mathcal{V}}_{\beta}\neq\emptyset\Longrightarrow\bigcap_{\beta\in B}Y_{\beta}\neq\emptyset (2.3)

for every finite B⊂AB\subset A.

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