Theorems · Definition · general topology

TopologicalSpace.compactlyGenerated

(X : Type w) → [TopologicalSpace X] → TopologicalSpace X

The compactly generated topology on a topological space X. This is the finest topology which makes all maps from compact Hausdorff spaces to X, which are continuous for the original topology, continuous. Note: this definition should be used with an explicit universe parameter u for the size of the compact Hausdorff spaces mapping to X.

Defined in

Mathlib.Topology.Compactness.CompactlyGeneratedSpace

Cited by

4 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpace