Theorems · Theorem · functional analysis
WithSeminorms.continuousSMul
∀ {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 → ContinuousSMul 𝕜 E- Cited by
- 0 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- NormedFieldstatement and proof · cited by 1,084
- ContinuousSMulstatement and proof · cited by 1,016
- WithSeminormsstatement and proof · cited by 69
- SeminormFamilystatement and proof · cited by 68
- SeminormFamily.moduleFilterBasisproof · cited by 10
- WithSeminorms.withSeminorms_eqproof · cited by 2
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