Theorems · Theorem · general topology
Homeomorph.isClosed_image
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (h : X ≃ₜ Y) {s : Set X},
IsClosed (⇑h '' s) ↔ IsClosed s- Defined in
- Mathlib.Topology.Homeomorph.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 75 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 and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.imagestatement · cited by 5,609
- IsClosedstatement and proof · cited by 1,639
- Homeomorphstatement and proof · cited by 725
- Homeomorph.symmproof · cited by 365
- Homeomorph.preimage_symmproof · cited by 9
- Homeomorph.isClosed_preimageproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- Homeomorph.isClosedMapproof · cited by 18
- ContinuousLinearEquiv.isClosed_imageproof · cited by 2
- AffineSubspace.isClosed_direction_iffproof · cited by 1
- IsCompact.isClosed_image_restrictproof · cited by 1
- IsClosed.isClosed_image_evalproof · cited by 0
- ContinuousLinearMap.closed_complemented_range_of_isCompl_of_ker_eq_botproof · cited by 0
- ContinuousAlgEquiv.isClosed_imageproof · cited by 0
- isClosedMap_restrict_of_compactSpaceproof · cited by 0