# Intersecting two staroidal products

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

Conjecture. ${\prod}^{\mathrm{Strd}}a\not\asymp {\prod}^{\mathrm{Strd}}b\iff b\in {\prod}^{\mathrm{Strd}}a\iff a\in {\prod}^{\mathrm{Strd}}b\iff \forall i\in n:{a}_{i}\not\asymp {b}_{i}$ for every $n$-indexed families $a$ and $b$ of filters on powersets.

The above conjecture has the below consequence (see my book for not so long proof).

Conjecture. Let $f$ is a staroid on powersets and $a\in {\prod}_{i\in \mathrm{arity}f}\mathrm{Src}{f}_{i}$, $b\in {\prod}_{i\in \mathrm{arity}f}\mathrm{Dst}{f}_{i}$. Then

$$\prod ^{\mathrm{Strd}}a\left[\prod ^{(C)}f\right]\prod ^{\mathrm{Strd}}b\iff \forall i\in n:{a}_{i}[{f}_{i}]{b}_{i}.$$ |

Title | Intersecting two staroidal products |
---|---|

Canonical name | IntersectingTwoStaroidalProducts |

Date of creation | 2013-03-22 19:50:13 |

Last modified on | 2013-03-22 19:50:13 |

Owner | porton (9363) |

Last modified by | porton (9363) |

Numerical id | 3 |

Author | porton (9363) |

Entry type | Conjecture |

Classification | msc 54J05 |

Classification | msc 54A05 |

Classification | msc 54D99 |

Classification | msc 54E05 |

Classification | msc 54E17 |

Classification | msc 54E99 |