Theorems · Theorem · general topology
Topology.IsInducing.continuous
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace Y] [inst_1 : TopologicalSpace X],
Topology.IsInducing f → Continuous f- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 48 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Continuousstatement · cited by 2,592
- Topology.IsInducingstatement and proof · cited by 266
- continuous_idproof · cited by 192
- Topology.IsInducing.continuous_iffproof · cited by 34
Cited by48
Results whose statement or proof uses this declaration.
- Topology.IsEmbedding.continuousproof · cited by 51
- Topology.IsInducing.isPreconnected_imageproof · cited by 11
- Topology.IsInducing.isCompact_iffproof · cited by 9
- IsDenseInducing.continuousproof · cited by 4
- Topology.IsInducing.regularSpaceproof · cited by 4
- Topology.IsInducing.isLindelof_iffproof · cited by 3
- AlgebraicGeometry.isBasis_basicOpenproof · cited by 3
- CommRingCat.HomTopology.isEmbedding_precomp_of_surjectiveproof · cited by 2
- Filter.continuous_nhdsproof · cited by 2
- TopologicalSpace.Opens.IsBasis.of_isInducingstatement and proof · cited by 2
- TopologicalSpace.Compacts.range_mapstatement · cited by 2
- Topology.IsInducing.perfectlyNormalSpaceproof · cited by 2