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Theorems · Theorem · general topology

BoundedContinuousFunction.restrict_apply

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

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : PseudoMetricSpace β]
  (f : BoundedContinuousFunction α β) (s : Set α) (x : ↑s), (f.domRestrict s) x = f ↑x

Alias of BoundedContinuousFunction.domRestrict_apply.

Defined in
Mathlib.Topology.ContinuousMap.Bounded.Basic
Cited by
0 results in Mathlib
Foundations
Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpacePseudoMetricSpace
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DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.Elem · cited by 7166Set.ElemPseudoMetricSpace · cited by 1550PseudoMetricSpaceBoundedContinuousFunction · cited by 511BoundedContinuousFunctionBoundedContinuousFunction.domRestrict · cited by 12BoundedContinuousFunction…BoundedContinuousFunction.domRestrict_apply · cited by 1BoundedContinuousFunction…BoundedContinuousFunction.res…CITED BYCITES

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