isOpen_iff_eventually

∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, IsOpen s ↔ ∀ x ∈ s, ∀ᶠ (y : X) in nhds x, y ∈ s

A set s is open iff for every point x in s and every y close to x, y is in s.

Defined in: Mathlib.Topology.Neighborhoods
Cited by: 3 results in Mathlib
Foundations: Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace

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