Theorems · Definition · general topology
BoundedContinuousFunction.const
(α : Type u) →
{β : Type v} → [inst : TopologicalSpace α] → [inst_1 : PseudoMetricSpace β] → β → BoundedContinuousFunction α βConstant as a continuous bounded function.
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- PseudoMetricSpacestatement and proof · cited by 1,550
- BoundedContinuousFunctionstatement · cited by 511
- ContinuousMap.constproof · cited by 45
Cited by21
Results whose statement or proof uses this declaration.
- BoundedContinuousFunction.const_applystatement and proof · cited by 9
- MeasureTheory.FiniteMeasure.testAgainstNN_conststatement · cited by 2
- MeasureTheory.FiniteMeasure.testAgainstNN_lipschitz_estimateproof · cited by 2
- BoundedContinuousFunction.add_norm_nonnegstatement · cited by 2
- exists_bounded_mem_Icc_of_closed_of_leproof · cited by 2
- BoundedContinuousFunction.integral_add_conststatement · cited by 2
- BoundedContinuousFunction.integral_const_substatement · cited by 2
- BoundedContinuousFunction.norm_const_lestatement · cited by 2
- BoundedContinuousFunction.norm_sub_nonnegstatement · cited by 2
- MeasureTheory.FiniteMeasure.testAgainstNN_zeroproof · cited by 1