Theorems · Theorem · general topology
IndiscreteTopology.of_forall_inseparable
∀ {α : Type u} [inst : TopologicalSpace α], (∀ (x y : α), Inseparable x y) → IndiscreteTopology α- Defined in
- Mathlib.Topology.Order
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- nhdsproof · cited by 5,554
- Inseparablestatement and proof · cited by 160
- mem_of_mem_nhdsproof · cited by 126
- top_uniqueproof · cited by 102
- IndiscreteTopologystatement · cited by 43
- TopologicalSpace.ext_nhdsproof · cited by 10
- nhds_topproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- TopologicalSpace.indiscrete_iff_forall_inseparableproof · cited by 3