Theorems · Theorem · general topology
Topology.IsEmbedding.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],
Topology.IsEmbedding g → Topology.IsEmbedding f → Topology.IsEmbedding (g ∘ f)- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Topology.IsEmbeddingstatement and proof · cited by 294
- Topology.IsInducingproof · cited by 266
- Topology.IsEmbedding.injectiveproof · cited by 103
- Topology.IsEmbedding.isInducingproof · cited by 47
- Topology.IsInducing.compproof · cited by 17
Cited by29
Results whose statement or proof uses this declaration.
- Topology.IsClosedEmbedding.compproof · cited by 14
- Topology.IsOpenEmbedding.compproof · cited by 12
- Topology.IsEmbedding.isStrictMap_iffproof · cited by 6
- LinearMap.isClosedEmbedding_of_injectiveproof · cited by 3
- TopCat.pullback_map_isEmbeddingproof · cited by 3
- Topology.IsEmbedding.compacts_mapproof · cited by 2
- CommRingCat.HomTopology.isEmbedding_precomp_of_surjectiveproof · cited by 2
- loc_compact_Haus_tot_disc_of_zero_dimproof · cited by 2
- TopCat.snd_isEmbedding_of_leftproof · cited by 2
- isEmbedding_of_iSup_eq_top_of_preimage_subset_rangeproof · cited by 1
- Topology.isEmbedding_iff_isStrictMap_injectiveproof · cited by 1
- ContinuousLinearMap.IsFredholm.of_isInvertible_restrictproof · cited by 1