Mathlib Map

Theorems · Theorem · general topology

Topology.IsClosedEmbedding.inclusion

∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X} (hst : s ⊆ t),
  IsClosed (Subtype.val ⁻¹' s) → Topology.IsClosedEmbedding (Set.inclusion hst)
Defined in
Mathlib.Topology.Constructions
Cited by
1 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

QuasiSober.of_subset · cited by 1QuasiSober.of_subsetSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.Elem · cited by 7166Set.ElemSet.preimage · cited by 4946Set.preimageIsClosed · cited by 1639IsClosedTopology.IsEmbedding · cited by 294Topology.IsEmbeddingTopology.IsClosedEmbedding · cited by 195Topology.IsClosedEmbeddingSet.inclusion · cited by 145Set.inclusionSet.range_inclusion · cited by 12Set.range_inclusionTopology.IsEmbedding.inclusion · cited by 8IsEmbedding.inclusionIsClosedEmbedding.inclusionCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.