http://openproblemgarden.org/op/funcolidal_products_inside_an_inward_reloid Comments for "Funcoidal products inside an inward reloid" en http://openproblemgarden.org/op/funcolidal_products_inside_an_inward_reloid <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; (solved) If <img class="teximage" src="/files/tex/0435b975c85d609a344bf2dcbd5cfacf4cccef40.png" alt="$ a \times^{\mathsf{\ensuremath{\operatorname{RLD}}}} b \subseteq \left( \mathsf{\ensuremath{\operatorname{RLD}}} \right)_{\ensuremath{\operatorname{in}}} f $" /> then <img class="teximage" src="/files/tex/540c8fb9c1b2fbbe12b46d35f6cb7aa3511a989b.png" alt="$ a \times^{\mathsf{\ensuremath{\operatorname{FCD}}}} b \subseteq f $" /> for every funcoid <img class="teximage" src="/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png" alt="$ f $" /> and atomic f.o. <img class="teximage" src="/files/tex/b1d91efbd5571a84788303f1137fb33fe82c43e2.png" alt="$ a $" /> and <img class="teximage" src="/files/tex/b94226d9717591da8122ae1467eda72a0f35d810.png" alt="$ b $" /> on the source and destination of <img class="teximage" src="/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png" alt="$ f $" /> correspondingly. </div> <p>A stronger conjecture:</p> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; If <img class="teximage" src="/files/tex/dbf9c288bef784da3d3a5d335b1ca97c01219f4e.png" alt="$ \mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{RLD}}}} \mathcal{B} \subseteq \left( \mathsf{\ensuremath{\operatorname{RLD}}} \right)_{\ensuremath{\operatorname{in}}} f $" /> then <img class="teximage" src="/files/tex/a4b67c268d0f2a939ae1d63a31fd57a3945e4ec5.png" alt="$ \mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{FCD}}}} \mathcal{B} \subseteq f $" /> for every funcoid <img class="teximage" src="/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png" alt="$ f $" /> and <img class="teximage" src="/files/tex/52f123c93b14e31b514495ac39d8781cd597c443.png" alt="$ \mathcal{A} \in \mathfrak{F} \left( \ensuremath{\operatorname{Src}}f \right) $" />, <img class="teximage" src="/files/tex/7310f0f823acdb77df75af0f8c924cdd8df0fe53.png" alt="$ \mathcal{B} \in \mathfrak{F} \left( \ensuremath{\operatorname{Dst}}f \right) $" />. </div> </tr></td> </table> </td> </tr> </table> Porton, Victor inward reloid Topology http://openproblemgarden.org/op/funcolidal_products_inside_an_inward_reloid#comment Sat, 31 Dec 2011 23:07:41 +0100 porton 37378 at http://openproblemgarden.org