Theorems · Theorem · general topology
IsOpen.relImage
∀ {α : Type ua} {β : Type ub} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {s : SetRel α β},
IsOpen s → ∀ {t : Set α}, IsOpen (s.image t)- Defined in
- Mathlib.Topology.UniformSpace.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.ofPredproof · cited by 6,101
- Set.iUnionproof · cited by 2,483
- IsOpenstatement and proof · cited by 2,400
- SetRelstatement and proof · cited by 581
- IsOpen.preimageproof · cited by 147
- SetRel.imagestatement · cited by 49
- isOpen_biUnionproof · cited by 35
- Continuous.prodMk_rightproof · cited by 32
- Set.ofPred_existsproof · cited by 23
Cited by3
Results whose statement or proof uses this declaration.
- TotallyBounded.nhds_vietoris_le_nhds_hausdorffproof · cited by 1
- TendstoUniformlyOn.upperHemicontinuousOnproof · cited by 1
- IsOpen.relPreimageproof · cited by 0