# nLab equivariant Tietze extension theorem

Contents

### Context

#### Representation theory

representation theory

geometric representation theory

# Contents

## Idea

A generalization of the Tietze extension theorem to equivariant functions provides conditions under which a continuous and equivariant function from a subspace of a topological G-space to another topological G-space has an extension to a continuous and equivariant function to the full $G$-space.

## Statement

###### Theorem

(Tietze-Gleason extension theorem)

Let

If

or

then $f$ has an extension to an equivariant continuous function $\widehat f$ on all of $X$.

$\array{ A &\overset{f}{\longrightarrow}& E \\ \cap & \nearrow_{\mathrlap{ \widehat{f} }} \\ X }$

## References

Last revised on August 20, 2019 at 16:08:10. See the history of this page for a list of all contributions to it.