Theorems · Theorem · general topology
Topology.IsEmbedding.injective
∀ {X : Type u_1} {Y : Type u_2} [tX : TopologicalSpace X] [tY : TopologicalSpace Y] {f : X → Y},
Topology.IsEmbedding f → Function.Injective fA topological embedding is injective.
- Defined in
- Mathlib.Topology.Defs.Induced
- Cited by
- 103 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 4 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
Cited by104
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.preimage_image_eqproof · cited by 37
- Topology.IsEmbedding.compproof · cited by 29
- Topology.IsEmbedding.of_compproof · cited by 16
- Topology.IsEmbedding.toHomeomorphproof · cited by 16
- Topology.IsClosedEmbedding.isClosed_iff_image_isClosedproof · cited by 13
- Topology.IsEmbedding.of_comp_iffproof · cited by 9
- Topology.IsOpenEmbedding.isOpen_iff_image_isOpenproof · cited by 7
- Topology.IsClosedEmbedding.isProperMapproof · cited by 6
- Topology.IsClosedEmbedding.map_tsumproof · cited by 6
- AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6
- Topology.IsEmbedding.discreteTopologyproof · cited by 6
- Topology.IsEmbedding.isStrictMap_iffproof · cited by 6