Theorems · Theorem · general topology
Ctop.mem_nhds_toTopsp
∀ {α : Type u_1} {σ : Type u_3} (F : Ctop α σ) {s : Set α} {a : α}, s ∈ nhds a ↔ ∃ b, a ∈ F.f b ∧ F.f b ⊆ s- Defined in
- Mathlib.Data.Analysis.Topology
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- Set.rangeproof · cited by 4,705
- Ctop.fstatement and proof · cited by 24
- Ctopstatement and proof · cited by 14
- TopologicalSpace.IsTopologicalBasis.mem_nhds_iffproof · cited by 13
- Ctop.toTopspstatement · cited by 8
- Ctop.toTopsp_isTopologicalBasisproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Ctop.Realizer.mem_nhdsproof · cited by 5
- Ctop.Realizer.ext'proof · cited by 1