Theorems · Theorem · general topology
TopologicalSpace.indiscrete_iff_forall_inseparable
∀ {α : Type u} {t : TopologicalSpace α}, IndiscreteTopology α ↔ ∀ (x y : α), Inseparable x y- Defined in
- Mathlib.Topology.Order
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Inseparablestatement · cited by 160
- IndiscreteTopologystatement and proof · cited by 43
- Inseparable.allproof · cited by 2
- IndiscreteTopology.of_forall_inseparableproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- TopologicalSpace.nontrivial_iff_exists_not_inseparableproof · cited by 4
- SeparationQuotient.inseparableSetoid_eq_top_iffproof · cited by 1
- TopologicalSpace.eq_top_iff_forall_inseparableproof · cited by 0