Theorems · Theorem · general topology
Topology.IsEmbedding.t1Space
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [T1Space Y] {f : X → Y},
Topology.IsEmbedding f → T1Space X- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 91 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
- T1Spacestatement and proof · cited by 275
- Topology.IsEmbedding.injectiveproof · cited by 103
- Topology.IsEmbedding.continuousproof · cited by 51
- t1Space_of_injective_of_continuousproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Homeomorph.t1Spaceproof · cited by 2
- Topology.IsClosedEmbedding.t4Spaceproof · cited by 1
- Topology.IsEmbedding.t5Spaceproof · cited by 1