Theorems · Theorem · general topology
Topology.IsOpenEmbedding.isOpenMap
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
Topology.IsOpenEmbedding f → IsOpenMap f- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- TopologicalSpacestatement and proof · cited by 24,529
- IsOpenMapstatement · cited by 253
- Topology.IsOpenEmbeddingstatement and proof · cited by 231
- Topology.IsEmbedding.isInducingproof · cited by 47
- Topology.IsOpenEmbedding.isOpen_rangeproof · cited by 33
- Topology.IsOpenEmbedding.isEmbeddingproof · cited by 22
- Topology.IsInducing.isOpenMapproof · cited by 1
Cited by52
Results whose statement or proof uses this declaration.
- Topology.IsOpenEmbedding.toOpenPartialHomeomorphproof · cited by 14
- IsOpen.isOpenMap_subtype_valproof · cited by 14
- Topology.IsOpenEmbedding.compproof · cited by 12
- Topology.IsOpenEmbedding.isOpen_iff_image_isOpenproof · cited by 7
- Topology.IsOpenEmbedding.isQuasiSeparated_iffproof · cited by 3
- Topology.IsOpenEmbedding.prodMapproof · cited by 3
- loc_compact_Haus_tot_disc_of_zero_dimproof · cited by 2
- Topology.isOpenEmbedding_iff_continuous_injective_isOpenMapproof · cited by 2
- Algebra.isOpen_smoothLocusproof · cited by 2
- IsPreirreducible.preimageproof · cited by 2
- Topology.IsOpenEmbedding.accPt_comap_iffproof · cited by 2
- AlgebraicGeometry.isLocallyArtinian_iff_openCoverproof · cited by 2