Theorems · Theorem · general topology
BoundedContinuousFunction.mkOfCompact_star
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : SeminormedAddCommGroup β]
[inst_2 : StarAddMonoid β] [inst_3 : NormedStarGroup β] [inst_4 : CompactSpace α] (f : C(α, β)),
BoundedContinuousFunction.mkOfCompact (star f) = star (BoundedContinuousFunction.mkOfCompact f)- Defined in
- Mathlib.Topology.ContinuousMap.Compact
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- ContinuousMapstatement and proof · cited by 2,491
- Star.starstatement · cited by 1,082
- CompactSpacestatement and proof · cited by 593
- BoundedContinuousFunctionstatement · cited by 511
- StarAddMonoidstatement and proof · cited by 296
- NormedStarGroupstatement and proof · cited by 54
- BoundedContinuousFunction.mkOfCompactstatement · cited by 21
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