Theorems · Theorem · general topology
OrderIso.continuous
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] [inst_2 : TopologicalSpace α]
[inst_3 : TopologicalSpace β] [OrderTopology α] [OrderTopology β] (e : α ≃o β), Continuous ⇑e- Cited by
- 6 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Preorderstatement and proof · cited by 7,952
- Set.ofPredproof · cited by 6,101
- Continuousstatement and proof · cited by 2,592
- IsOpenproof · cited by 2,400
- Set.Ioiproof · cited by 1,463
- OrderTopologystatement and proof · cited by 1,355
- Set.Iioproof · cited by 1,166
- OrderIsostatement and proof · cited by 874
- OrderIso.symmproof · cited by 475
Cited by6
Results whose statement or proof uses this declaration.
- Real.continuousOn_logproof · cited by 17
- Real.continuous_arcsinproof · cited by 8
- ENNReal.continuous_expproof · cited by 4
- NNReal.continuous_sqrtproof · cited by 3
- ContinuousMap.exists_extension_forall_mem_of_isClosedEmbeddingproof · cited by 1
- ENNReal.continuous_logproof · cited by 1