Theorems · Definition · general topology

stoneCechExtend

{α : Type u} →
  [inst : TopologicalSpace α] →
    {β : Type v} →
      [inst_1 : TopologicalSpace β] → [T2Space β] → {g : α → β} → Continuous g → [CompactSpace β] → StoneCech α → β

The extension of a continuous function from α to a compact Hausdorff space β to the Stone-Čech compactification of α. This extension implements the universal property of this compactification.

Defined in

Mathlib.Topology.Compactification.StoneCech

Cited by

6 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceT2SpaceCompactSpace