An Introduction to Manifolds

Part of the series Universitext pp 127-134

Bump Functions and Partitions of Unity

* Final gross prices may vary according to local VAT.

Get Access

The existence of a C partition of unity is one of the most important technical tools in the theory of C manifolds. It is the single feature that makes the behavior of C manifolds so different from real-analytic or complex manifolds. In this chapter we construct C bump functions on any manifold and prove the existence of a C∞ partition of unity on a compact manifold. The proof of the existence of a C partition of unity on a general manifold is more technical and is postponed to Appendix C.