Theorems · Theorem · functional analysis

moduleTopology_le

∀ (R : Type u_1) [inst : TopologicalSpace R] (A : Type u_2) [inst_1 : Add A] [inst_2 : SMul R A]
  [τA : TopologicalSpace A] [ContinuousSMul R A] [ContinuousAdd A], moduleTopology R A ≤ τA

The module topology is ≤ any topology making A into a topological module.

Defined in

Mathlib.Topology.Algebra.Module.ModuleTopology

Cited by

2 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceAddSMulTopologicalSpaceContinuousSMulContinuousAdd