Theorems · Theorem · functional analysis
norm_lt_iff_of_nonempty_compactlySupported
∀ {α : Type u_1} {γ : Type u_2} [inst : TopologicalSpace α] [inst_1 : NonUnitalNormedRing γ] [c : Nonempty α]
{f : BoundedContinuousFunction α γ}, f ∈ compactlySupported α γ → ∀ {M : ℝ}, ‖f‖ < M ↔ ∀ (x : α), ‖f x‖ < M- Cited by
- 0 results in Mathlib
- Foundations
- Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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 and proof · cited by 5,413
- norm_nonnegproof · cited by 725
- LT.lt.trans_leproof · cited by 678
- BoundedContinuousFunctionstatement and proof · cited by 511
- LT.lt.not_geproof · cited by 305
- NonUnitalNormedRingstatement and proof · cited by 231
- lt_or_geproof · cited by 182
- Classical.arbitraryproof · cited by 161
- TwoSidedIdealstatement · cited by 151
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