An open base {B_i} for a topological space X is the class of open sets in X in which any open set in X is the union of sets in {B_i}.(adsbygoogle = window.adsbygoogle || []).push({});

Please consider the following and tell me if i am wrong

observation

An open cover in X is a subclass of some given open base for X. This then should imply that an open cover for X is abasic open covercontained in some given open base.This is because of the definition above and an open cover is a class of open sets whose union contains X

conclusion

Every open cover for a topological space X is a basic opencover. i am saying that an open cover must be contained in some given open base

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Basic open cover

Loading...

Similar Threads - Basic open cover | Date |
---|---|

I Basic Q about Vector/tensor definition and velocity | Feb 24, 2018 |

A Very basic question about cohomology. | Jan 25, 2017 |

More (VERY BASIC) Questions on Example on Wedge Products | Feb 4, 2016 |

Simple/Basic Example on Wedge Products | Feb 4, 2016 |

Transversality of a Vector Field in terms of Forms (Open Books) | Dec 28, 2013 |

**Physics Forums - The Fusion of Science and Community**