Theorems · Theorem · functional analysis
comap_norm_nhds_zero
∀ {E : Type u_4} [inst : SeminormedAddGroup E], Filter.comap norm (nhds 0) = nhds 0- Defined in
- Mathlib.Analysis.Normed.Group.Continuity
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 118 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
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Norm.normstatement · cited by 5,413
- Filter.comapstatement and proof · cited by 546
- SeminormedAddGroupstatement and proof · cited by 331
- dist_zero_rightproof · cited by 172
- nhds_comap_distproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- norm_withSeminormsproof · cited by 12
- Complex.comap_exp_nhds_zeroproof · cited by 4
- SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInfproof · cited by 3
- SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInfproof · cited by 1
- Seminorm.uniformSpace_eq_of_hasBasisproof · cited by 1
- comap_norm_nhdsGT_zeroproof · cited by 1
- LinearMap.mem_span_iff_boundproof · cited by 0