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Theorems · Definition · general topology

BoundedContinuousFunction.const

(α : Type u) →
  {β : Type v} → [inst : TopologicalSpace α] → [inst_1 : PseudoMetricSpace β] → β → BoundedContinuousFunction α β

Constant as a continuous bounded function.

Defined in
Mathlib.Topology.ContinuousMap.Bounded.Basic
Cited by
20 results in Mathlib
Foundations
Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpacePseudoMetricSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

BoundedContinuousFunction.const_apply · cited by 9BoundedContinuousFunction…MeasureTheory.FiniteMeasure.testAgainstNN_const · cited by 2FiniteMeasure.testAgainst…MeasureTheory.FiniteMeasure.testAgainstNN_lipschitz_estimate · cited by 2FiniteMeasure.testAgainst…BoundedContinuousFunction.add_norm_nonneg · cited by 2BoundedContinuousFunction…exists_bounded_mem_Icc_of_closed_of_le · cited by 2exists_bounded_mem_Icc_of…BoundedContinuousFunction.integral_add_const · cited by 2BoundedContinuousFunction…BoundedContinuousFunction.integral_const_sub · cited by 2BoundedContinuousFunction…BoundedContinuousFunction.norm_const_le · cited by 2BoundedContinuousFunction…BoundedContinuousFunction.norm_sub_nonneg · cited by 2BoundedContinuousFunction…BoundedContinuousFunction.exists_extension_forall_mem_of_isClosedEmbedding · cited by 2BoundedContinuousFunction…MeasureTheory.FiniteMeasure.testAgainstNN_zero · cited by 1FiniteMeasure.testAgainst…BoundedContinuousFunction.tendsto_integral_of_forall_integral_le_liminf_integral · cited by 1BoundedContinuousFunction…BoundedContinuousFunction.tendsto_integral_of_forall_limsup_integral_le_integral · cited by 1BoundedContinuousFunction…BoundedContinuousFunction.norm_const_eq · cited by 1BoundedContinuousFunction…BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_isClosedEmbedding · cited by 1BoundedContinuousFunction…TopologicalSpace · cited by 24529TopologicalSpacePseudoMetricSpace · cited by 1550PseudoMetricSpaceBoundedContinuousFunction · cited by 511BoundedContinuousFunctionContinuousMap.const · cited by 45ContinuousMap.constBoundedContinuousFunction.con…CITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by21

Results whose statement or proof uses this declaration.