# rotund space

A normed space is said to be rotund if every point of $C(0,1)$ is an extreme point. Here $C(0,1)$ is the set $\{b:\parallel b\parallel =1\}$. Equivalently, a space is rotund if and only if $a\ne b$ and $\parallel a\parallel =\parallel b\parallel \le 1$ implies $$.

A uniformly convex space is rotund.

Title | rotund space |
---|---|

Canonical name | RotundSpace |

Date of creation | 2013-03-22 16:04:56 |

Last modified on | 2013-03-22 16:04:56 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 8 |

Author | Mathprof (13753) |

Entry type | Definition |

Classification | msc 46H05 |