Theorems · Theorem · functional analysis
SchwartzMap.continuous
∀ {E : Type u_5} {F : Type u_6} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : NormedAddCommGroup F]
[inst_3 : NormedSpace ℝ F] (f : SchwartzMap E F), Continuous ⇑fEvery Schwartz function is continuous.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Continuousstatement · cited by 2,592
- SchwartzMapstatement and proof · cited by 251
- ContDiff.continuousproof · cited by 23
- SchwartzMap.smoothproof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- SchwartzMap.integrableproof · cited by 10
- SchwartzMap.toBoundedContinuousFunctionproof · cited by 5
- SchwartzMap.memLpproof · cited by 3
- SchwartzMap.memLp_topproof · cited by 1
- SchwartzMap.injective_toLpproof · cited by 0
- SchwartzMap.convolution_applyproof · cited by 0
- SchwartzMap.norm_toBoundedContinuousFunction_leproof · cited by 0
- SchwartzMap.tsum_eq_tsum_fourierproof · cited by 0