http://openproblemgarden.org/op/upgrading_a_completary_multifuncoid Comments for "Upgrading a completary multifuncoid" en http://openproblemgarden.org/op/upgrading_a_completary_multifuncoid <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> <p> Let <img class="teximage" src="/files/tex/8a60ffddf5f015b5658f273c0698af378fdebbde.png" alt="$ \mho $" /> be a set, <img class="teximage" src="/files/tex/2f80186ad9cd0260fcf25f804b47e285791e195e.png" alt="$ \mathfrak{F} $" /> be the set of filters on <img class="teximage" src="/files/tex/8a60ffddf5f015b5658f273c0698af378fdebbde.png" alt="$ \mho $" /> ordered reverse to set-theoretic inclusion, <img class="teximage" src="/files/tex/9598b289a66ea54ae8fb1d473e47c550777c77b6.png" alt="$ \mathfrak{P} $" /> be the set of principal filters on <img class="teximage" src="/files/tex/8a60ffddf5f015b5658f273c0698af378fdebbde.png" alt="$ \mho $" />, let <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" /> be an index set. Consider the filtrator <img class="teximage" src="/files/tex/a5edcd29d9b038aa8123878c4a318d959874fba4.png" alt="$ \left( \mathfrak{F}^n ; \mathfrak{P}^n \right) $" />.</p> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; If <img class="teximage" src="/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png" alt="$ f $" /> is a completary multifuncoid of the form <img class="teximage" src="/files/tex/81d0b4bc571faee2e8f352e99db8b54be6f9bb4f.png" alt="$ \mathfrak{P}^n $" />, then <img class="teximage" src="/files/tex/93b48164cf5af924121c451b6bb17268ae140bae.png" alt="$ E^{\ast} f $" /> is a completary multifuncoid of the form <img class="teximage" src="/files/tex/34e3ea9e5283eb80b19513453991c07af9c98f8a.png" alt="$ \mathfrak{F}^n $" />. </div> <p>See below for definition of all concepts and symbols used to in this conjecture.</p> <p>Refer to <a href="http://www.mathematics21.org/algebraic-general-topology.html">this Web site</a> for the theory which I now attempt to generalize.</p> </tr></td> </table> </td> </tr> </table> Porton, Victor Topology http://openproblemgarden.org/op/upgrading_a_completary_multifuncoid#comment Sat, 04 Feb 2012 15:54:16 +0100 porton 37385 at http://openproblemgarden.org