Theorems · Theorem · general topology
ContinuousMapClass.map_continuous
∀ {F : Type u_1} {X : outParam (Type u_2)} {Y : outParam (Type u_3)} {inst : TopologicalSpace X}
{inst_1 : TopologicalSpace Y} {inst_2 : FunLike F X Y} [self : ContinuousMapClass F X Y] (f : F), Continuous ⇑fContinuity
- Defined in
- Mathlib.Topology.ContinuousMap.Defs
- Cited by
- 119 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 7 definitions · uses no axioms
- Assumes
- ContinuousMapClass
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.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Continuousstatement · cited by 2,592
- FunLikestatement and proof · cited by 2,560
- ContinuousMapClassstatement and proof · cited by 31
Cited by120
Results whose statement or proof uses this declaration.
- toContinuousMapproof · cited by 99
- Real.continuous_probCharproof · cited by 5
- Path.continuous_uncurry_iffproof · cited by 4
- HasFDerivWithinAt.limproof · cited by 4
- ProbabilityTheory.IsGaussianProcess.isPreBrownianReal_of_covarianceproof · cited by 4
- Measure.ext_of_integral_prod_mul_prod_boundedContinuousFunctionproof · cited by 4
- isCompact_setOfPred_finiteMeasure_le_of_compactSpaceproof · cited by 3
- indepFun_pi_of_prod_bcfproof · cited by 3
- cfcₙHom_eq_cfcₙ_extendproof · cited by 3
- HasFDerivAtFilter.of_comp_of_leftInverseproof · cited by 3
- FormalMultilinearSeries.partialSum_continuousproof · cited by 3
- Unitization.cfcₙ_eq_cfc_inrproof · cited by 3