Theorems · Definition · general topology
ContinuousMap.toFun
{X : Type u_1} → {Y : Type u_2} → [inst : TopologicalSpace X] → [inst_1 : TopologicalSpace Y] → C(X, Y) → X → YThe function X → Y
- Defined in
- Mathlib.Topology.ContinuousMap.Defs
- Cited by
- 72 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- ContinuousMapstatement and proof · cited by 2,491
Cited by120
Results whose statement or proof uses this declaration.
- ContinuousMap.continuous_toFunstatement · cited by 47
- Path.extproof · cited by 30
- TopCat.toSSetObj₀Equivproof · cited by 18
- CompactlySupportedContinuousMap.nnrealPartproof · cited by 15
- IsCoveringMap.exists_path_liftsproof · cited by 4
- CompactlySupportedContinuousMap.hasCompactSupport'statement · cited by 4
- GenLoop.currySumproof · cited by 4
- continuousOn_cfcproof · cited by 4
- Path.mk.congr_simpstatement and proof · cited by 4
- BoundedContinuousFunction.map_bounded'statement · cited by 4
- LightProfinite.epi_iff_surjectiveproof · cited by 3
- LocallyConstant.comap_injectivestatement and proof · cited by 3