Theorems · Theorem · Lie groups

denseRange_zsmul_iff_surjective

∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : AddCommGroup G] [inst_2 : LinearOrder G] [IsOrderedAddMonoid G]
  [OrderTopology G] {a : G}, (DenseRange fun x => x • a) ↔ Function.Surjective fun x => x • a

In a linearly ordered additive group, the integer multiples of an element are dense iff they are the whole group.

Defined in

Mathlib.Topology.Algebra.Order.Group

Cited by

1 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceAddCommGroupLinearOrderIsOrderedAddMonoidOrderTopology