Theorems · Theorem · general topology
Topology.IsEmbedding.t0Space
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [T0Space Y] {f : X → Y},
Topology.IsEmbedding f → T0Space X- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 and proof · cited by 294
- T0Spacestatement and proof · cited by 179
- Topology.IsEmbedding.injectiveproof · cited by 103
- Topology.IsEmbedding.continuousproof · cited by 51
- t0Space_of_injective_of_continuousproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Topology.IsEmbedding.t3Spaceproof · cited by 3
- Homeomorph.t0Spaceproof · cited by 1
- Topology.IsEmbedding.metrizableSpaceproof · cited by 1
- Topology.IsOpenEmbedding.spectralSpaceproof · cited by 0
- Topology.IsEmbedding.t6Spaceproof · cited by 0