Theorems · Theorem · general topology
Equiv.induced_symm
∀ {α : Type u_4} {β : Type u_5} (e : α ≃ β), TopologicalSpace.induced ⇑e.symm = TopologicalSpace.coinduced ⇑e- Defined in
- Mathlib.Topology.Order
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Equivstatement and proof · cited by 8,337
- Set.preimageproof · cited by 4,946
- Equiv.symmstatement and proof · cited by 3,681
- IsOpenproof · cited by 2,400
- TopologicalSpace.inducedstatement · cited by 148
- TopologicalSpace.coinducedstatement · cited by 56
- Equiv.image_symm_eq_preimageproof · cited by 17
- TopologicalSpace.extproof · cited by 15
- isOpen_coinducedproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- LinearMap.continuous_of_isClosed_kerproof · cited by 2
- Equiv.coinduced_symmproof · cited by 2
- IsClosed.isClopenableproof · cited by 1