https://www.openproblemgarden.org/op/strict_inequalities_for_products_of_filters Comments for "Strict inequalities for products of filters" en https://www.openproblemgarden.org/op/strict_inequalities_for_products_of_filters <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/porton_victor">Porton</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/topology">Topology</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; <img class="teximage" src="/files/tex/333c9bbd34eb26a9a813d527283c1b038b247af3.png" alt="$ \mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{RLD}}}}_F \mathcal{B} \subset \mathcal{A} \ltimes \mathcal{B} \subset \mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{RLD}}}} \mathcal{B} $" /> for some filter objects <img class="teximage" src="/files/tex/3abde4ab7e21fe6fad91d0a03ad306c2c82659d9.png" alt="$ \mathcal{A} $" />, <img class="teximage" src="/files/tex/cca7b496bd14e6acf10041305acbd75cd720f9b3.png" alt="$ \mathcal{B} $" />. Particularly, is this formula true for <img class="teximage" src="/files/tex/34af23595994335e2e2b76a7cd787c6fce57e186.png" alt="$ \mathcal{A} = \mathcal{B} = \Delta \cap \uparrow^{\mathbb{R}} \left( 0 ; + \infty \right) $" />? </div> <p>A weaker conjecture:</p> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; <img class="teximage" src="/files/tex/64050fc1df5a7d5bc9cf7f4f90fe71a78d003a0b.png" alt="$ \mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{RLD}}}}_F \mathcal{B} \subset \mathcal{A} \ltimes \mathcal{B} $" /> for some filter objects <img class="teximage" src="/files/tex/3abde4ab7e21fe6fad91d0a03ad306c2c82659d9.png" alt="$ \mathcal{A} $" />, <img class="teximage" src="/files/tex/cca7b496bd14e6acf10041305acbd75cd720f9b3.png" alt="$ \mathcal{B} $" />. </div> </tr></td> </table> </td> </tr> </table> Porton, Victor filter products Topology https://www.openproblemgarden.org/op/strict_inequalities_for_products_of_filters#comment Tue, 09 Aug 2011 22:35:12 +0200 porton 37339 at https://www.openproblemgarden.org