Theorems · Theorem · general topology
Filter.Frequently.mem_closure
∀ {X : Type u} [inst : TopologicalSpace X] {x : X} {s : Set X}, (∃ᶠ (x : X) in nhds x, x ∈ s) → x ∈ closure sAlias of the reverse direction of mem_closure_iff_frequently.
- Defined in
- Mathlib.Topology.Neighborhoods
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 64 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.
Cites6
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 · cited by 5,554
- closurestatement · cited by 1,254
- Filter.Frequentlystatement · cited by 414
- mem_closure_iff_frequentlyproof · cited by 15
Cited by5
Results whose statement or proof uses this declaration.
- IsLUB.mem_closureproof · cited by 6
- Filter.Frequently.mem_of_closedproof · cited by 5
- IsGLB.mem_closureproof · cited by 5
- mem_closure_of_frequently_of_tendstoproof · cited by 4
- ContinuousMap.sublattice_closure_eq_topproof · cited by 1