Theorems · Theorem · general topology

AntilipschitzWith.properSpace

∀ {β : Type u_2} [inst : PseudoMetricSpace β] {α : Type u_4} [inst_1 : MetricSpace α] {K : NNReal} {f : α → β}
  [ProperSpace α], AntilipschitzWith K f → Continuous f → Function.Surjective f → ProperSpace β

The image of a proper space under an expanding onto map is proper.

Defined in

Mathlib.Topology.MetricSpace.Antilipschitz

Cited by

1 results in Mathlib

Foundations

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

Assumes

PseudoMetricSpaceMetricSpaceProperSpace