Theorems · Theorem · general topology
Topology.IsOpenEmbedding.isInducing
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
Topology.IsOpenEmbedding f → Topology.IsInducing f- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.IsInducingstatement · cited by 266
- Topology.IsOpenEmbeddingstatement and proof · cited by 231
- Topology.IsEmbedding.isInducingproof · cited by 47
- Topology.IsOpenEmbedding.isEmbeddingproof · cited by 22
Cited by14
Results whose statement or proof uses this declaration.
- Topology.IsOpenEmbedding.locallyCompactSpaceproof · cited by 3
- Topology.IsLocallyConstructible.of_isOpenCoverproof · cited by 3
- JacobsonSpace.of_isOpenEmbeddingproof · cited by 3
- Topology.IsOpenEmbedding.quasiSoberproof · cited by 2
- Topology.IsOpenEmbedding.compacts_mapproof · cited by 1
- MeasureTheory.Measure.Regular.comap'proof · cited by 1
- Topology.IsOpenEmbedding.generalizingMapproof · cited by 1
- Topology.IsInducing.sumSwapproof · cited by 1
- Topology.IsOpenEmbedding.preimage_closedPointsproof · cited by 1
- MeasureTheory.Measure.InnerRegular.comap'proof · cited by 1
- OnePoint.continuous_map_iffproof · cited by 1
- OnePoint.comap_coe_nhdsproof · cited by 0