# product of uniform spaces

###### Definition.

Let ${\{{X}_{\alpha}\}}_{\alpha \in I}$ be a nonempty family of uniform spaces. The is the weakest uniformity (http://planetmath.org/UniformitiesOnASetFormACompleteLattice) on the Cartesian product $X={\prod}_{\alpha \in I}{X}_{\alpha}$ making all the projection maps ${\pi}_{\alpha}:X\to {X}_{\alpha}$ uniformly continuous^{}.

Title | product of uniform spaces |
---|---|

Canonical name | ProductOfUniformSpaces |

Date of creation | 2013-03-22 16:30:49 |

Last modified on | 2013-03-22 16:30:49 |

Owner | mps (409) |

Last modified by | mps (409) |

Numerical id | 4 |

Author | mps (409) |

Entry type | Definition |

Classification | msc 54E15 |