nLab
paracompact manifold

Contents

Contents

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

Last revised on May 12, 2014 at 00:25:33. See the history of this page for a list of all contributions to it.