# Intersection with a staroid product through its upper sets

Prerequisites: \hrefhttp://www.mathematics21.org/algebraic-general-topology.htmlAlgebraic General Topology.

Conjecture. Let $\U0001d509$ is a family of sets of filters on distributive lattices with least elements. Let $a\in \prod \U0001d509$, $S\in \mathcal{P}\prod \U0001d509$ is a generalized filter base, $\bigsqcup S=a$, $f$ is a staroid of the form $\prod \U0001d509$. Then

$$\prod ^{\mathrm{Strd}(\U0001d509)}a\not\asymp f\iff \forall A\in S:\prod ^{\mathrm{Strd}(\U0001d504)}A\not\asymp f.$$ |

(This conjecture may be weakened for the special case of filters on powersets.)

Title | Intersection^{} with a staroid product^{} through its upper sets |
---|---|

Canonical name | IntersectionWithAStaroidProductThroughItsUpperSets |

Date of creation | 2013-03-22 19:48:39 |

Last modified on | 2013-03-22 19:48:39 |

Owner | porton (9363) |

Last modified by | porton (9363) |

Numerical id | 2 |

Author | porton (9363) |

Entry type | Conjecture |

Classification | msc 54J05 |

Classification | msc 54A05 |

Classification | msc 54D99 |

Classification | msc 54E05 |

Classification | msc 54E17 |

Classification | msc 54E99 |