Theorems · Theorem · functional analysis
SeminormFamily.basisSets_mem_nhds
∀ {𝕜 : Type u_11} {E : Type u_12} {ι : Type u_13} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] (p : SeminormFamily 𝕜 E ι),
(∀ (i : ι), Continuous ⇑(p i)) → ∀ U ∈ p.basisSets, U ∈ nhds 0If a family of seminorms is continuous, then their basis sets are neighborhoods of zero.
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- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
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