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Let Σ be the point-line truncation of an augmented  J -Grassmann geometry of a spherical building  B . We show that if | J | = 1, or if | J | ≥ 2 and some additional conditions hold, then the convex subspace closure in Σ of the point shadow of an apartment of  B  is the entire space Σ.

Convex subspace closure of the point shadow of an apartment of a spherical building