Theorems · Theorem · general topology
IsClosedMap.restrictPreimage
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β},
IsClosedMap f → ∀ (s : Set β), IsClosedMap (s.restrictPreimage f)- Defined in
- Mathlib.Topology.LocalAtTarget
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement and proof · cited by 7,166
- Set.imageproof · cited by 5,609
- Set.preimagestatement and proof · cited by 4,946
- IsClosedproof · cited by 1,639
- IsClosedMapstatement and proof · cited by 138
- Set.restrictPreimagestatement and proof · cited by 84
- Set.image_restrictPreimageproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- IsProperMap.restrictPreimageproof · cited by 2
- isQuotientCoveringMap_npowproof · cited by 2
- TopologicalSpace.IsOpenCover.isClosedMap_iff_restrictPreimageproof · cited by 0
- IsOpenMap.finite_connectedComponents_of_finite_preimage_singletonproof · cited by 0