### Abstract

Given the unit sphere Sn, we prove the following theorem and several extensions: For any continuous function f : Sn - Sn, if f has no fixed point in Sn, then f must be surjective.

Original language | English |
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Place of Publication | Tilburg |

Publisher | Microeconomics |

Number of pages | 6 |

Volume | 1999-75 |

Publication status | Published - 1999 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 1999-75 |

### Keywords

- Surjective function
- fixed point
- antifexed point
- antipodal point
- sphere
- manifold

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## Cite this

Sun, N., & Yang, Z. F. (1999).

*Surjective Function Theorems*. (CentER Discussion Paper; Vol. 1999-75). Microeconomics.