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[Merged by Bors] - feat(analysis/locally_convex): first countable topologies from countable families of seminorms#16595
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[Merged by Bors] - feat(analysis/locally_convex): first countable topologies from countable families of seminorms#16595
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| lemma with_seminorms.has_countable_basis (hp : with_seminorms p) : | ||
| (𝓝 (0 : E)).has_countable_basis (λ _, true) | ||
| (λ i : finset ι × ℕ, ball (i.fst.sup p) 0 (i.snd + 1)⁻¹) := |
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Do you care about the specific basis or do you only use that for showing that this filter is countably generated. If the latter, you could simply use with_seminorms_iff_nhds_eq_infi and then apply filter.comap.is_countably_generated and filter.infi.is_countably_generated
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I am not entirely certain that the first lemma is not used anywhere, but it does not feel to useful.
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Co-authored-by: Anatole Dedecker <anatolededecker@gmail.com>
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🚀 Pull request has been placed on the maintainer queue by ADedecker. |
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Thanks! bors r+ |
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…ble families of seminorms (#16595) This PR proves that if the topology is induced by a countable family of seminorms, then it is first countable.
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This PR proves that if the topology is induced by a countable family of seminorms, then it is first countable.