Theorems · Theorem · general topology
nhdsSet_inj_iff
∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] {s t : Set X}, nhdsSet s = nhdsSet t ↔ s = t- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT1Space
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
- Filterstatement · cited by 8,121
- T1Spacestatement and proof · cited by 275
- nhdsSetstatement · cited by 267
- nhdsSet_le_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- injective_nhdsSetproof · cited by 1