Theorems · Theorem · general topology
Topology.IsEmbedding.of_comp
∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} {f : X → Y} {g : Y → Z} [inst : TopologicalSpace X]
[inst_1 : TopologicalSpace Y] [inst_2 : TopologicalSpace Z],
Continuous f → Continuous g → Topology.IsEmbedding (g ∘ f) → Topology.IsEmbedding f- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Continuousstatement and proof · cited by 2,592
- Topology.IsEmbeddingstatement and proof · cited by 294
- Topology.IsInducingproof · cited by 266
- Topology.IsEmbedding.injectiveproof · cited by 103
- Function.Injective.of_compproof · cited by 82
- Topology.IsEmbedding.isInducingproof · cited by 47
- Topology.IsInducing.of_compproof · cited by 11
Cited by16
Results whose statement or proof uses this declaration.
- TopCat.pullback_map_isEmbeddingproof · cited by 3
- Topology.IsEmbedding.of_leftInverseproof · cited by 3
- Topology.IsEmbedding.codRestrictproof · cited by 3
- CommRingCat.HomTopology.isEmbedding_precomp_of_surjectiveproof · cited by 2
- isEmbedding_prodMkRightproof · cited by 2
- isEmbedding_graphproof · cited by 1
- isEmbedding_of_iSup_eq_top_of_preimage_subset_rangeproof · cited by 1
- Topology.IsEmbedding.units_mapproof · cited by 1
- RestrictedProduct.isEmbedding_inclusion_principalproof · cited by 1
- RestrictedProduct.isEmbedding_inclusion_topproof · cited by 1
- Topology.IsEmbedding.specialLinearGroup_mapproof · cited by 1
- Topology.IsEmbedding.restrictproof · cited by 1