Theorems · Theorem · functional analysis
balancedCore_mem_nhds_zero
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NormedDivisionRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] [ContinuousSMul 𝕜 E] {U : Set E} [(nhdsWithin 0 {0}ᶜ).NeBot],
U ∈ nhds 0 → balancedCore 𝕜 U ∈ nhds 0- Cited by
- 4 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realproof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Norm.normproof · cited by 5,413
- Filter.Tendstoproof · cited by 3,814
- Compl.complstatement and proof · cited by 2,925
- one_mulproof · cited by 2,841
- nhdsWithinstatement and proof · cited by 1,912
Cited by4
Results whose statement or proof uses this declaration.
- nhds_basis_balancedproof · cited by 10
- nhds_hasBasis_absConvexproof · cited by 2
- unique_topology_of_t2proof · cited by 1
- nhds_basis_closed_balancedproof · cited by 0