Theorems · Theorem · commutative algebra

isLinearTopology_iff_hasBasis_open_submodule

∀ {R : Type u_1} {M : Type u_3} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [inst_3 : TopologicalSpace M] [ContinuousAdd M],
  IsLinearTopology R M ↔ (nhds 0).HasBasis (fun N => IsOpen ↑N) fun N => ↑N

Defined in

Mathlib.Topology.Algebra.LinearTopology

Cited by

1 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleTopologicalSpaceContinuousAdd