Theorems · Theorem · general topology
BoundedContinuousFunction.continuous
∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : PseudoMetricSpace β]
(f : BoundedContinuousFunction α β), Continuous ⇑f- Cited by
- 26 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- PseudoMetricSpacestatement and proof · cited by 1,550
- BoundedContinuousFunctionstatement and proof · cited by 511
- ContinuousMap.continuousproof · cited by 74
- BoundedContinuousFunction.toContinuousMapproof · cited by 19
Cited by26
Results whose statement or proof uses this declaration.
- BoundedContinuousFunction.integrableproof · cited by 9
- indicator_indepFun_pi_of_prod_bcfproof · cited by 4
- BoundedContinuousFunction.toReal_lintegral_coe_eq_integralproof · cited by 3
- MeasureTheory.tendsto_lintegral_nn_filter_of_le_constproof · cited by 3
- MeasureTheory.FiniteMeasure.tendsto_of_forall_integral_tendstoproof · cited by 3
- MeasureTheory.continuous_diracProbaproof · cited by 2
- MeasureTheory.ProbabilityMeasure.tendsto_map_of_tendsto_of_continuousproof · cited by 2
- BoundedContinuousFunction.measurable_coe_ennreal_compproof · cited by 2