Theorems · Theorem · general topology
Topology.IsEmbedding.metrizableSpace
∀ {X : Type u_2} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
[TopologicalSpace.MetrizableSpace Y] {f : X → Y}, Topology.IsEmbedding f → TopologicalSpace.MetrizableSpace XGiven an embedding of a topological space into a metrizable space, the source space is also metrizable.
- Defined in
- Mathlib.Topology.Metrizable.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- TopologicalSpace.PseudoMetrizableSpaceproof · cited by 245
- T0Spaceproof · cited by 179
- Topology.IsEmbedding.toIsInducingproof · cited by 48
- TopologicalSpace.MetrizableSpacestatement and proof · cited by 39
- Topology.IsEmbedding.t0Spaceproof · cited by 5
- Topology.IsInducing.pseudoMetrizableSpaceproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.