# nLab C-infinity topology

### Context

#### Topology

topology

algebraic topology

## Examples

#### Differential geometry

differential geometry

synthetic differential geometry

mapping space

# Contents

## Idea

The Whitney $C^k$ topology is a topology on the set $C^\infty(X,Y)$ of smooth functions between two smooth manifolds, induced from the natural topology of the order-$k$ jet spaces of maps from $X$ to $Y$.

Often, and espcially for $k = \infty$ this is just called the $C^k$-topology .

## References

• Kriegl, Michor, …

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Revised on April 21, 2014 06:35:18 by Mike Shulman (108.247.151.163)