Theorems · Theorem · Lie groups

denseRange_zpow_iff_surjective

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

In a linearly ordered multiplicative group, the integer powers 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

TopologicalSpaceCommGroupLinearOrderIsOrderedMonoidOrderTopology