Theorems · Theorem · general topology
isClosedMap_restrict_of_compactSpace
∀ {ι : Type u_1} {α : ι → Type u_2} {S : Set ι} [inst : (i : ι) → TopologicalSpace (α i)]
[∀ (i : ι), CompactSpace (α i)], IsClosedMap S.domRestrict- Defined in
- Mathlib.Topology.IsClosedRestrict
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceCompactSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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
- IsClosedproof · cited by 1,639
- CompactSpacestatement and proof · cited by 593
- Set.domRestrictstatement and proof · cited by 383
- Set.image_compproof · cited by 142
- IsClosedMapstatement · cited by 138
- Homeomorph.isClosed_imageproof · cited by 8
- Homeomorph.piEquivPiSubtypeProdproof · cited by 3
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.