http://openproblemgarden.org/op/funcoid_corresponding_to_reloid_through_lattice_gamma Comments for "Funcoid corresponding to reloid through lattice Gamma" en http://openproblemgarden.org/op/funcoid_corresponding_to_reloid_through_lattice_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; For every reloid <img class="teximage" src="/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png" alt="$ f $" /> and <img class="teximage" src="/files/tex/1f01dd9f1243b55507248bea7af215e6469c00a8.png" alt="$ \mathcal{X} \in \mathfrak{F} (\operatorname{Src} f) $" />, <img class="teximage" src="/files/tex/d7fa63ea4e0a3ad7a7f39a92a95ae4fe1906197d.png" alt="$ \mathcal{Y} \in \mathfrak{F} (\operatorname{Dst} f) $" />:<br /> <ol class="enumerate"> \item <img class="teximage" src="/files/tex/2f0c7dbaa1a5747d9bca753501374e8cd2500318.png" alt="$ \mathcal{X} \mathrel{[(\mathsf{FCD}) f]} \mathcal{Y} \Leftrightarrow \forall F \in \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f : \mathcal{X} \mathrel{[F]} \mathcal{Y} $" />; \item <img class="teximage" src="/files/tex/bcc925b41f94370c0dfe32107235c7a3435dcbf9.png" alt="$ \langle (\mathsf{FCD}) f \rangle \mathcal{X} = \bigcap_{F \in \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f} \langle F \rangle \mathcal{X} $" />. </ol> </div> <p>It's proved by me 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 funcoid corresponding to reloid Topology http://openproblemgarden.org/op/funcoid_corresponding_to_reloid_through_lattice_gamma#comment Fri, 26 Sep 2014 21:41:52 +0200 porton 59967 at http://openproblemgarden.org