Theorems · Theorem · commutative algebra

IsCentralScalar.isLinearTopology_iff

∀ (R : Type u_1) {M : Type u_3} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [inst_3 : TopologicalSpace M] [inst_4 : Module Rᵐᵒᵖ M] [IsCentralScalar R M],
  IsLinearTopology Rᵐᵒᵖ M ↔ IsLinearTopology R M

If the left and right actions of R on M coincide, then a topology is Rᵐᵒᵖ-linear if and only if it is R-linear.

Defined in

Mathlib.Topology.Algebra.LinearTopology

Cited by

0 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleTopologicalSpaceModuleIsCentralScalar