Theorems · Theorem · general topology

isProperMap_iff_tendsto_cocompact

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [T2Space Y]
  [CompactlyCoherentSpace Y] {f : X → Y},
  IsProperMap f ↔ Continuous f ∧ Filter.Tendsto f (Filter.cocompact X) (Filter.cocompact Y)

Version of isProperMap_iff_isCompact_preimage in terms of cocompact. There was an older version of this theorem which was changed to this one to make use of the CompactlyGeneratedSpace typeclass. (since 2024-11-10)

Defined in

Mathlib.Topology.Maps.Proper.CompactlyGenerated

Cited by

2 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceT2SpaceCompactlyCoherentSpace