Theorems · Theorem · general topology
Topology.IsEmbedding.inclusion
∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X} (h : s ⊆ t), Topology.IsEmbedding (Set.inclusion h)- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 78 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.
Cites7
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 · cited by 7,166
- Topology.IsEmbeddingstatement · cited by 294
- Set.inclusionstatement · cited by 145
- Topology.IsEmbedding.subtypeValproof · cited by 41
- Topology.IsEmbedding.codRestrictproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- TopologicalSpace.IsSeparable.secondCountableTopologyproof · cited by 4
- TopologicalSpace.NoetherianSpace.of_subsetproof · cited by 2
- Topology.IsOpenEmbedding.inclusionproof · cited by 2
- Topology.IsClosedEmbedding.inclusionproof · cited by 1
- DiscreteTopology.of_subsetproof · cited by 1
- TopologicalSpace.Opens.isOpenEmbedding_of_leproof · cited by 1
- StarSubalgebra.isClosedEmbedding_inclusionproof · cited by 0
- isLocalHomeomorphOn_iff_isOpenEmbedding_restrictproof · cited by 0