Theorems · Theorem · general topology
Topology.IsEmbedding.continuous
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
Topology.IsEmbedding f → Continuous f- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 51 results in Mathlib
- Foundations
- Depth 76 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.IsEmbeddingstatement and proof · cited by 294
- Topology.IsInducing.continuousproof · cited by 48
- Topology.IsEmbedding.isInducingproof · cited by 47
Cited by51
Results whose statement or proof uses this declaration.
- Topology.IsClosedEmbedding.continuousproof · cited by 25
- Topology.IsOpenEmbedding.continuousproof · cited by 23
- ENNReal.continuous_coeproof · cited by 18
- TopologicalSpace.NonemptyCompacts.continuous_toCompactsproof · cited by 8
- Topology.IsOpenEmbedding.isOpen_iff_image_isOpenproof · cited by 7
- Topology.IsEmbedding.discreteTopologyproof · cited by 6
- Topology.IsEmbedding.aestronglyMeasurable_comp_iffproof · cited by 6
- TopologicalSpace.NonemptyCompacts.continuous_coeproof · cited by 5
- Topology.IsEmbedding.t0Spaceproof · cited by 5
- Topology.IsEmbedding.t2Spaceproof · cited by 5
- TopologicalSpace.Compacts.continuous_coeproof · cited by 4
- UpperHalfPlane.continuous_coeproof · cited by 4