http://openproblemgarden.org/op/rld_in_through_gamma Comments for "Inner reloid through the lattice Gamma" en http://openproblemgarden.org/op/rld_in_through_gamma <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/9c5b448dbc0964ca844d30e92247626e8d5420b5.png" alt="$ (\mathsf{RLD})_{\operatorname{in}} f = \bigcap^{\mathsf{RLD}} \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f $" /> for every funcoid <img class="teximage" src="/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png" alt="$ f $" />. </div> <p>Counter-example: <img class="teximage" src="/files/tex/6fddad405926bcf21d3d0a2635cab152f8275f8d.png" alt="$ (\mathsf{RLD})_{\operatorname{in}} f \sqsubset \bigcap^{\mathsf{RLD}} \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f $" /> for the funcoid <img class="teximage" src="/files/tex/d2fc25cd45a40aa6b1bf7e9d792d137bee613610.png" alt="$ f = (=)|_\mathbb{R} $" /> is proved in <a href="http://www.mathematics21.org/binaries/funcoids-are-filters.pdf">this online article</a>.</p> </tr></td> </table> </td> </tr> </table> Porton, Victor filters funcoids inner reloid reloids Topology http://openproblemgarden.org/op/rld_in_through_gamma#comment Thu, 25 Sep 2014 20:50:28 +0200 porton 59963 at http://openproblemgarden.org