Theorems · Theorem · general topology
Topology.IsClosedEmbedding.continuous
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
Topology.IsClosedEmbedding f → Continuous f- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 77 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.IsClosedEmbeddingstatement and proof · cited by 195
- Topology.IsEmbedding.continuousproof · cited by 51
- Topology.IsClosedEmbedding.isEmbeddingproof · cited by 25
Cited by25
Results whose statement or proof uses this declaration.
- Topology.IsClosedEmbedding.isClosed_iff_image_isClosedproof · cited by 13
- Topology.IsClosedEmbedding.isProperMapproof · cited by 6
- Topology.IsClosedEmbedding.map_tsumproof · cited by 6
- Matrix.IsHermitian.cfc_eqproof · cited by 3
- Topology.IsClosedEmbedding.closure_image_eqproof · cited by 3
- isCompact_setOfPred_finiteMeasure_le_of_isCompactproof · cited by 2
- Topology.IsClosedEmbedding.map_tprodproof · cited by 2
- ContinuousMap.exists_extensionstatement · cited by 2
- Topology.IsClosedEmbedding.normalSpaceproof · cited by 2
- BoundedContinuousFunction.exists_extension_norm_eq_of_isClosedEmbeddingproof · cited by 2
- Topology.IsClosedEmbedding.paracompactSpaceproof · cited by 1