Theorems · Theorem · functional analysis
LinearMap.toSeminorm_ball_zero
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E] {f : E →ₗ[𝕜] 𝕜}
{r : ℝ}, f.toSeminorm.ball 0 r = {x | ‖f x‖ < r}- Defined in
- Mathlib.Analysis.LocallyConvex.WeakDual
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Set.ofPredstatement and proof · cited by 6,101
- Norm.normstatement and proof · cited by 5,413
- NormedFieldstatement and proof · cited by 1,084
- Seminorm.ballstatement · cited by 78
- Seminorm.ball_zero_eqproof · cited by 7
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