nLab paracompact manifold

Definition

A paracompact manifold is a topological space that is

1. a paracompact space;

2. a manifold.

Properties

Theorem

Every paracompact smooth manifold admits a complete Riemannian metric with bounded absolute sectional curvature and positive injectivity radius.

This is shown in (Greene).

References

• R. Greene, Complete metrics of bounded curvature on noncompact manifolds Archiv der Mathematik Volume 31, Number 1