Theorems · Theorem · general topology
Topology.IsOpenEmbedding.toIsEmbedding
∀ {X : Type u_1} {Y : Type u_2} [tX : TopologicalSpace X] [tY : TopologicalSpace Y] {f : X → Y},
Topology.IsOpenEmbedding f → Topology.IsEmbedding f- Defined in
- Mathlib.Topology.Defs.Induced
- Cited by
- 61 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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 · cited by 294
- Topology.IsOpenEmbeddingstatement and proof · cited by 231
Cited by61
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.preimage_image_eqproof · cited by 37
- Topology.IsOpenEmbedding.isEmbeddingproof · cited by 22
- Topology.IsOpenEmbedding.compproof · cited by 12
- Topology.IsOpenEmbedding.isOpen_iff_image_isOpenproof · cited by 7
- AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6
- Topology.IsEmbedding.inlproof · cited by 5
- Topology.IsEmbedding.inrproof · cited by 5
- Topology.IsOpenEmbedding.image_mem_nhdsproof · cited by 4
- Topology.IsOpenEmbedding.isOpenMap_iffproof · cited by 4
- AlgebraicGeometry.Scheme.IdealSheafData.le_support_iff_le_vanishingIdealproof · cited by 4
- Topology.IsOpenEmbedding.isQuasiSeparated_iffproof · cited by 3
- Topology.IsOpenEmbedding.prodMapproof · cited by 3