Theorems · Inductive type · general topology
NontrivialTopology
(α : Type u_2) → [TopologicalSpace α] → Prop
A topological space is nontrivial if it is not the indiscrete topology.
- Defined in
- Mathlib.Topology.Order
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by48
Results whose statement or proof uses this declaration.
- LinearIsometry.norm_toContinuousLinearMapstatement and proof · cited by 13
- NormedSpace.sphere_nonemptystatement and proof · cited by 8
- exists_norm_ne_zerostatement and proof · cited by 6
- ContinuousLinearMap.norm_idstatement and proof · cited by 5
- nontrivialTopology_iff_exists_nnnorm_ne_zerostatement · cited by 4
- TopologicalSpace.nontrivial_iff_exists_not_inseparablestatement · cited by 4
- exists_norm_eqstatement and proof · cited by 4
- LinearIsometry.enorm_toContinuousLinearMapstatement and proof · cited by 3
- ContinuousLinearMap.homothety_normstatement and proof · cited by 3
- nontrivialTopology_iff_exists_nnnorm_ne_zero'statement · cited by 3
- nontrivialTopology_iff_exists_norm_ne_zerostatement · cited by 3
- nontrivialTopology_iff_exists_norm_ne_zero'statement · cited by 3