Theorems · Theorem · general topology
TopologicalSpace.Opens.coe_comap
∀ {α : Type u_2} {β : Type u_3} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] (f : C(α, β))
(U : TopologicalSpace.Opens β), ↑((TopologicalSpace.Opens.comap f) U) = ⇑f ⁻¹' ↑U- Defined in
- Mathlib.Topology.Sets.Opens
- Cited by
- 1 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.
Cites9
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 and proof · cited by 24,529
- SetLike.coestatement · cited by 8,199
- Set.preimagestatement · cited by 4,946
- ContinuousMapstatement and proof · cited by 2,491
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- FrameHomstatement · cited by 70
- TopologicalSpace.Opens.comapstatement · cited by 32
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.exists_range_eq_of_isConstructibleproof · cited by 1