nLab
paracompact manifold

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

Revised on May 12, 2014 00:25:33 by Urs Schreiber (217.39.7.253)