Theorems · Theorem · general topology

HasCompactMulSupport.is_one_at_infty

∀ {α : Type u_2} {γ : Type u_5} [inst : TopologicalSpace α] [inst_1 : One γ] {f : α → γ} [inst_2 : TopologicalSpace γ],
  HasCompactMulSupport f → Filter.Tendsto f (Filter.cocompact α) (nhds 1)

If f has compact multiplicative support, then f tends to 1 at infinity.

Defined in

Mathlib.Topology.Algebra.Support

Cited by

1 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceOneTopologicalSpace