Theorems · Theorem · functional analysis
WithSeminorms.hasBasis_ball
∀ {𝕜 : Type u_2} {E : Type u_6} {ι : Type u_9} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] {p : SeminormFamily 𝕜 E ι},
WithSeminorms p → ∀ {x : E}, (nhds x).HasBasis (fun sr => 0 < sr.2) fun sr => (sr.1.sup p).ball x sr.2- Cited by
- 2 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- Finsetstatement and proof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- Filterproof · cited by 8,121
- Set.imageproof · cited by 5,609
- nhdsstatement and proof · cited by 5,554
- add_zeroproof · cited by 2,707
- HVAdd.hVAddproof · cited by 1,820
- IsTopologicalAddGroupproof · cited by 1,394
Cited by2
Results whose statement or proof uses this declaration.
- WithSeminorms.mem_nhds_iffproof · cited by 2
- WithSeminorms.tendsto_nhds'proof · cited by 1