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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.

Defined in
Mathlib.Topology.Algebra.Module.ModuleTopology
Cited by
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Foundations
Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceAddSMul

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