Theorems · Theorem · functional analysis
ModuleTopology.continuousSMul
∀ (R : Type u_1) [inst : TopologicalSpace R] (A : Type u_2) [inst_1 : Add A] [inst_2 : SMul R A], ContinuousSMul R A
Scalar multiplication • : R × A → A is continuous if R is a topological
ring, and A is an R module with the module topology.
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- 0 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceAddSMul
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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
- Set.ofPredproof · cited by 6,101
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousAddproof · cited by 777
- moduleTopologystatement · cited by 9
- continuousSMul_sInfproof · cited by 2
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