Theorems · Theorem · general topology
TopologicalSpace.nontrivial_iff_exists_not_inseparable
∀ {α : Type u} {t : TopologicalSpace α}, NontrivialTopology α ↔ ∃ x y, ¬Inseparable x y- Defined in
- Mathlib.Topology.Order
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 70 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
- Iff.notproof · cited by 489
- Inseparablestatement · cited by 160
- NontrivialTopologystatement · cited by 46
- TopologicalSpace.indiscrete_iff_forall_inseparableproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- nontrivialTopology_iff_exists_nnnorm_ne_zeroproof · cited by 4
- NontrivialTopology.of_exists_not_inseparableproof · cited by 0
- NontrivialTopology.exists_not_inseparableproof · cited by 0
- TopologicalSpace.ne_top_iff_exists_not_inseparableproof · cited by 0