Theorems · Theorem · Lie groups

not_denseRange_zpow

∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : CommGroup G] [inst_2 : LinearOrder G] [IsOrderedMonoid G]
  [OrderTopology G] [Nontrivial G] [DenselyOrdered G] {a : G}, ¬DenseRange fun x => a ^ x

In a nontrivial densely linearly ordered commutative group, the integer powers of an element can't be dense.

Defined in

Mathlib.Topology.Algebra.Order.Group

Cited by

1 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceCommGroupLinearOrderIsOrderedMonoidOrderTopologyNontrivialDenselyOrdered