Theorems · Theorem · general topology
ContinuousMap.apply_le_norm
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : CompactSpace α] (f : C(α, ℝ)) (x : α), f x ≤ ‖f‖- Defined in
- Mathlib.Topology.ContinuousMap.Compact
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceCompactSpace
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Norm.normstatement · cited by 5,413
- ContinuousMapstatement and proof · cited by 2,491
- le_reflproof · cited by 2,061
- le_transproof · cited by 985
- CompactSpacestatement and proof · cited by 593
- ContinuousMap.norm_coe_le_normproof · cited by 14
- le_absproof · cited by 5
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