Theorems · Theorem · general topology

ProperSpace.of_seq_closedBall

∀ {α : Type u} [inst : PseudoMetricSpace α] {β : Type u_3} {l : Filter β} [l.NeBot] {x : α} {r : β → ℝ},
  Filter.Tendsto r l Filter.atTop → (∀ᶠ (i : β) in l, IsCompact (Metric.closedBall x (r i))) → ProperSpace α

If there exists a sequence of compact closed balls with the same center such that the radii tend to infinity, then the space is proper.

Defined in

Mathlib.Topology.MetricSpace.ProperSpace

Cited by

2 results in Mathlib

Foundations

Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpaceFilter.NeBot