interior — Mathlib

English

For a 0-simplex, the interior is empty.

Русский

Для 0-симплекса interior пуст.

LaTeX

$$$ s.\mathrm{interior} = \emptyset $ for a 0-simplex$$

Lean4

/-- The interior of a simplex is the set of points that can be expressed as an affine combination
of the vertices with weights strictly between 0 and 1. This is equivalent to the intrinsic
interior of the convex hull of the vertices. -/
protected def interior {n : ℕ} (s : Simplex k P n) : Set P :=
  s.setInterior (Set.Ioo 0 1)

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