Theorems · Theorem · general topology
Topology.IsClosedEmbedding.isClosedEmbedding_iff_continuous_injective_isClosedMap
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
Topology.IsClosedEmbedding f ↔ Continuous f ∧ Function.Injective f ∧ IsClosedMap f- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 2,592
- Topology.IsClosedEmbeddingstatement and proof · cited by 195
- IsClosedMapstatement and proof · cited by 138
- Topology.IsEmbedding.injectiveproof · cited by 103
- Topology.IsClosedEmbedding.toIsEmbeddingproof · cited by 27
- Topology.IsClosedEmbedding.continuousproof · cited by 25
- Topology.IsClosedEmbedding.isClosedMapproof · cited by 19
- Topology.IsClosedEmbedding.of_continuous_injective_isClosedMapproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Topology.IsClosedEmbedding.sumElimproof · cited by 0