Theorems · Theorem · general topology

isClosed_iff_forall_filter

∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X},
  IsClosed s ↔ ∀ (x : X) (F : Filter X), F.NeBot → F ≤ Filter.principal s → F ≤ nhds x → x ∈ s

Defined in

Mathlib.Topology.ClusterPt

Cited by

3 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpace