Theorems · Theorem · general topology
isOpen_coinduced
∀ {α : Type u_1} {β : Type u_2} {t : TopologicalSpace α} {s : Set β} {f : α → β}, IsOpen s ↔ IsOpen (f ⁻¹' s)- Defined in
- Mathlib.Topology.Order
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 65 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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.preimagestatement · cited by 4,946
- IsOpenstatement · cited by 2,400
- TopologicalSpace.coinducedstatement · cited by 56
Cited by12
Results whose statement or proof uses this declaration.
- isClosed_coinducedproof · cited by 5
- isOpenMap_quotient_mk'_addproof · cited by 3
- isOpenMap_quotient_mk'_mulproof · cited by 3
- Equiv.induced_symmproof · cited by 3
- LocallyPathConnectedSpace.coinducedproof · cited by 2
- QuotientGroup.discreteTopology_iffproof · cited by 2
- QuotientAddGroup.discreteTopology_iffproof · cited by 2
- IsClosed.isClopenableproof · cited by 1
- FiberPrebundle.isOpen_sourceproof · cited by 1
- ULift.isOpen_iffproof · cited by 1
- UCompactlyGeneratedSpace.isOpenproof · cited by 1
- alexandrovDiscrete_coinducedproof · cited by 0