symm_map_nhdsWithin_image — Mathlib

English

The inverse map reverses the nhdsWithin-image correspondence: map I^{-1} (nhdsWithin (I x) (I s)) = nhdsWithin s x.

Русский

Обратное отображение восстанавливает correspondences: map I^{-1} (nhdsWithin (I x) (I s)) = nhdsWithin s x.

LaTeX

$$map I^{-1} (nhdsWithin (I x) (I'' s)) = nhdsWithin s x$$

Lean4

theorem symm_map_nhdsWithin_image {x : H} {s : Set H} : map I.symm (𝓝[I '' s] I x) = 𝓝[s] x := by
  rw [← I.map_nhdsWithin_eq, map_map, I.symm_comp_self, map_id]

Похожие утверждения