Theorems · Theorem · general topology
genericPoints.component_injective
∀ {α : Type u_1} [inst : TopologicalSpace α] [T0Space α], Function.Injective genericPoints.component- Defined in
- Mathlib.Topology.Sober
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT0Space
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 · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement and proof · cited by 7,166
- T0Spacestatement and proof · cited by 179
- irreducibleComponentsstatement · cited by 35
- genericPointsstatement and proof · cited by 10
- genericPoints.componentstatement and proof · cited by 7
- IsGenericPoint.eqproof · cited by 4
- genericPoints.isGenericPointproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- genericPoints.ofComponent_componentproof · cited by 0
- genericPoints.finiteproof · cited by 0