Theorems · Theorem · general topology
IsClosed.isClosedEmbedding_subtypeVal
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, IsClosed s → Topology.IsClosedEmbedding Subtype.val- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- IsClosedstatement and proof · cited by 1,639
- Topology.IsClosedEmbeddingstatement · cited by 195
- Topology.IsClosedEmbedding.subtypeValproof · cited by 4
Cited by19
Results whose statement or proof uses this declaration.
- IsClosed.isClosedMap_subtype_valproof · cited by 8
- IsClosed.polishSpaceproof · cited by 6
- NNReal.isClosedEmbedding_coeproof · cited by 4
- IsClosed.tendsto_coe_cofinite_of_isDiscreteproof · cited by 4
- Matrix.SpecialLinearGroup.isClosedEmbedding_valproof · cited by 2
- loc_compact_Haus_tot_disc_of_zero_dimproof · cited by 2
- BoundedContinuousFunction.exists_norm_eq_domRestrict_eq_of_closedproof · cited by 1
- Stonean.extremallyDisconnected_preimageproof · cited by 1
- IsClosed.isCompletelyPseudoMetrizableSpaceproof · cited by 1
- IsClosed.isProperMap_subtypeValproof · cited by 1
- IsCompactOperator.codRestrictproof · cited by 1
- BoundedContinuousFunction.exists_forall_mem_domRestrict_eq_of_closedproof · cited by 1