nhdsWithin — Mathlib

English

The neighborhood within filter nhdsWithin x s collects neighborhoods of x restricted to s; it is the intersection of nhds x with the principal filter of s.

Русский

Фильтр окрестностей внутри nhdsWithin x s собирает окрестности x, ограниченные внутри s; это пересечение nhds x и принциипи s.

LaTeX

$$$nhdsWithin(x,s) = nhds(x) \\sqcap 𝓟(s)$$$

Lean4

/-- The "neighborhood within" filter. Elements of `𝓝[s] x` are sets containing the
intersection of `s` and a neighborhood of `x`. -/
def nhdsWithin (x : X) (s : Set X) : Filter X :=
  𝓝 x ⊓ 𝓟 s

Похожие утверждения