# Kontinuitätssatz

###### Theorem.

$G\subset {\u2102}^{n}$ is pseudoconvex if and only if for any family of closed analytic discs ${\mathrm{\{}{d}_{\alpha}\mathrm{\}}}_{\alpha \mathrm{\in}I}$ in $G$ with ${\mathrm{\cup}}_{\alpha \mathrm{\in}I}\mathrm{\partial}\mathit{}{d}_{\alpha}$ being a relatively compact set in $G$ then ${\mathrm{\cup}}_{\alpha \mathrm{\in}I}{d}_{\alpha}$ is also a relatively compact set in $G$.

This is the analogue of one of the definitions of a convex set. Just replace
pseudoconvex with convex and closed analytic discs with closed line segments^{}.

## References

- 1 M. Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild. , Princeton University Press, Princeton, New Jersey, 1999.
- 2 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.

Title | Kontinuitätssatz |
---|---|

Canonical name | Kontinuitatssatz |

Date of creation | 2013-03-22 15:49:15 |

Last modified on | 2013-03-22 15:49:15 |

Owner | jirka (4157) |

Last modified by | jirka (4157) |

Numerical id | 5 |

Author | jirka (4157) |

Entry type | Theorem |

Classification | msc 32T05 |

Synonym | Hartogs Kontinuitätssatz |

Synonym | Kontinuitatssatz |