Theorems · Theorem · general topology
Filter.Frequently.mem_of_closed
∀ {X : Type u} [inst : TopologicalSpace X] {x : X} {s : Set X}, (∃ᶠ (x : X) in nhds x, x ∈ s) → IsClosed s → x ∈ s- Defined in
- Mathlib.Topology.Neighborhoods
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- nhdsstatement and proof · cited by 5,554
- IsClosedstatement and proof · cited by 1,639
- Filter.Frequentlystatement and proof · cited by 414
- IsClosed.closure_subsetproof · cited by 11
- Filter.Frequently.mem_closureproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- IsClosed.mem_of_frequently_of_tendstoproof · cited by 5
- Dense.upperBounds_imageproof · cited by 2
- ContinuousMapZero.nonUnitalStarAlgHom_apply_mul_eq_zeroproof · cited by 1
- ContinuousMapZero.mul_nonUnitalStarAlgHom_apply_eq_zeroproof · cited by 1
- IsClosed.mem_of_mapClusterPtproof · cited by 1