Theorems · Theorem · general topology
WithTopology.nontrivialTopology_iff
∀ {α : Type u} {t : TopologicalSpace α}, NontrivialTopology (WithTopology α t) ↔ t ≠ ⊤- Defined in
- Mathlib.Topology.Order
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- Top.topstatement and proof · cited by 9,680
- TopologicalSpace.inducedproof · cited by 148
- NontrivialTopologystatement · cited by 46
- WithTopologystatement and proof · cited by 30
- induced_composeproof · cited by 26
- WithTopology.ofTopologyproof · cited by 18
- induced_topproof · cited by 2
- WithTopology.topology_eq_inducedproof · cited by 1
- induced_fun_idproof · cited by 1
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