# topology of locally convex spaces is generated by seminorms

Theorem - Let $V$ be a topological vector space^{} over $\mathbb{R}$ or $\u2102$. Then $V$ is locally convex (http://planetmath.org/LocallyConvexTopologicalVectorSpace) if and only if the topology^{} of $V$ is a family of seminorms^{}.

Moreover, $V$ is Hausdorff^{} and locally if and only if the topology of $V$ is a family of seminorms.

Title | topology of locally convex spaces is generated by seminorms |
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Canonical name | TopologyOfLocallyConvexSpacesIsGeneratedBySeminorms |

Date of creation | 2013-03-22 17:43:29 |

Last modified on | 2013-03-22 17:43:29 |

Owner | asteroid (17536) |

Last modified by | asteroid (17536) |

Numerical id | 4 |

Author | asteroid (17536) |

Entry type | Theorem |

Classification | msc 46-00 |

Classification | msc 46A03 |