Theorems · Theorem · general topology
image_eq_zero_of_notMem_tsupport
∀ {X : Type u_1} {α : Type u_2} [inst : Zero α] [inst_1 : TopologicalSpace X] {f : X → α} {x : X},
x ∉ tsupport f → f x = 0- Defined in
- Mathlib.Topology.Algebra.Support
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ZeroTopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- tsupportstatement and proof · cited by 178
- Function.support_subset_iff'proof · cited by 35
- subset_tsupportproof · cited by 21
Cited by24
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.hasDerivAt_of_bilinearproof · cited by 4
- integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrableproof · cited by 2
- HasCompactSupport.is_zero_at_inftyproof · cited by 2
- Continuous.memLp_of_hasCompactSupportproof · cited by 2
- HasCompactSupport.continuous_convolution_rightproof · cited by 1
- TemperedDistribution.isVanishingOn_deltaproof · cited by 1
- exist_norm_eqproof · cited by 1
- NNRealRMK.le_rieszMeasure_of_isCompact_tsupport_subsetproof · cited by 1