Theorems · Theorem · functional analysis
continuous_norm
∀ {E : Type u_4} [inst : SeminormedAddGroup E], Continuous fun a => ‖a‖- Defined in
- Mathlib.Analysis.Normed.Group.Continuity
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
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.
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- Continuousstatement and proof · cited by 2,592
- SeminormedAddGroupstatement and proof · cited by 331
- continuous_constproof · cited by 278
- continuous_idproof · cited by 192
- dist_zero_rightproof · cited by 172
- Continuous.distproof · cited by 20
Cited by36
Results whose statement or proof uses this declaration.
- Continuous.normproof · cited by 45
- MeasureTheory.AEStronglyMeasurable.normproof · cited by 30
- continuous_nnnormproof · cited by 9
- MeasureTheory.StronglyMeasurable.normproof · cited by 7
- measurable_normproof · cited by 6
- WithSeminorms.continuous_seminormproof · cited by 5
- Complex.continuousAt_argproof · cited by 3
- continuousAt_clogproof · cited by 2
- norm_le_gronwallBound_of_norm_deriv_right_leproof · cited by 2
- Complex.continuousWithinAt_arg_of_re_neg_of_im_zeroproof · cited by 2
- hasFDerivWithinAt_closure_of_tendsto_fderivproof · cited by 2