Theorems · Definition · general topology

BoundedContinuousFunction.restrict

Deprecated since 2026-07-19Use BoundedContinuousFunction.domRestrict instead.

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

Alias of BoundedContinuousFunction.domRestrict. Restrict the domain of a bounded continuous function to a set.

Defined in: Mathlib.Topology.ContinuousMap.Bounded.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace PseudoMetricSpace

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Setstatement · cited by 53,352
TopologicalSpacestatement · cited by 24,529
Set.Elemstatement · cited by 7,166
PseudoMetricSpacestatement · cited by 1,550
BoundedContinuousFunctionstatement · cited by 511
BoundedContinuousFunction.domRestrictproof · cited by 12

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