Theorems · Theorem · general topology
TopologicalSpace.Closeds.singleton_injective
∀ {α : Type u_2} [inst : TopologicalSpace α] [inst_1 : T1Space α], Function.Injective fun x => {x}- Defined in
- Mathlib.Topology.Sets.Closeds
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpaceT1Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- T1Spacestatement and proof · cited by 275
- TopologicalSpace.Closedsstatement · cited by 168
- Function.Injective.of_compproof · cited by 82
- Set.singleton_injectiveproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- TopologicalSpace.Closeds.singleton_injproof · cited by 0