Theorems · Theorem · commutative algebra

IsLinearTopology.hasBasis_open_subbimodule

∀ (R : Type u_1) (R' : Type u_2) {M : Type u_3} [inst : Ring R] [inst_1 : Ring R'] [inst_2 : AddCommGroup M]
  [inst_3 : Module R M] [inst_4 : Module R' M] [SMulCommClass R R' M] [inst_6 : TopologicalSpace M] [ContinuousAdd M]
  [IsLinearTopology R M] [IsLinearTopology R' M],
  (nhds 0).HasBasis (fun I => IsOpen ↑I ∧ (∀ (r : R), ∀ x ∈ I, r • x ∈ I) ∧ ∀ (r' : R'), ∀ x ∈ I, r' • x ∈ I) fun I =>
    ↑I

A variant of IsLinearTopology.hasBasis_subbimodule using IsOpen I instead of I ∈ 𝓝 0.

Defined in

Mathlib.Topology.Algebra.LinearTopology

Cited by

0 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingRingAddCommGroupModuleModuleSMulCommClassTopologicalSpaceContinuousAddIsLinearTopologyIsLinearTopology