Theorems · Theorem · general topology
DeltaGeneratedSpace.isOpen_iff
Deprecated since 2026-04-23Use Topology.IsGeneratedBy.isOpen_iff instead.
∀ {ι : Type t} (X : ι → Type u) [inst : (i : ι) → TopologicalSpace (X i)] {Y : Type v} [tY : TopologicalSpace Y]
[Topology.IsGeneratedBy X Y] {U : Set Y}, IsOpen U ↔ ∀ ⦃i : ι⦄ (f : C(X i, Y)), IsOpen (⇑f ⁻¹' U)Alias of Topology.IsGeneratedBy.isOpen_iff.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- TopologicalSpacestatement · cited by 24,529
- Set.preimagestatement · cited by 4,946
- ContinuousMapstatement · cited by 2,491
- IsOpenstatement · cited by 2,400
- Topology.IsGeneratedBystatement · cited by 38
- Topology.IsGeneratedBy.isOpen_iffproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.