http://openproblemgarden.org/op/graph_product_of_multifuncoids Comments for "Graph product of multifuncoids" en http://openproblemgarden.org/op/graph_product_of_multifuncoids <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; Let <img class="teximage" src="/files/tex/bfff269cc7df9bdb7c57d8b6a2a74020d114f24d.png" alt="$ F $" /> is a family of multifuncoids such that each <img class="teximage" src="/files/tex/468bb283d323c2779688c7954a9de964d909524f.png" alt="$ F_i $" /> is of the form <img class="teximage" src="/files/tex/ec2677105f186d63c73702433a4fe09bcc1e92bc.png" alt="$ \lambda j \in N \left( i \right) : \mathfrak{F} \left( U_j \right) $" /> where <img class="teximage" src="/files/tex/ccbc2dd2c65699e06cafe73a1ded06b193ab52f0.png" alt="$ N \left( i \right) $" /> is an index set for every <img class="teximage" src="/files/tex/ca49c241ece07915c97a31774a977841c6f0414c.png" alt="$ i $" /> and <img class="teximage" src="/files/tex/246b680371106f172aa027bc2c18e977aa2c779b.png" alt="$ U_j $" /> is a set for every <img class="teximage" src="/files/tex/282a1b4a166eb4c8018038a9ca0d509b2c90b79b.png" alt="$ j $" />. Let every <img class="teximage" src="/files/tex/2e6c4a540867fd2ef352ea31f20e7d00c81d8b07.png" alt="$ F_i = E^{\ast} f_i $" /> for some multifuncoid <img class="teximage" src="/files/tex/3d8d4274a2a88f65b70123aab5f541cbfb114eb2.png" alt="$ f_i $" /> of the form <img class="teximage" src="/files/tex/0154473bda09e018c819cbf7c181386972c20d4a.png" alt="$ \lambda j \in N \left( i \right) : \mathfrak{P} \left( U_j \right) $" /> regarding the filtrator <img class="teximage" src="/files/tex/3be7158866e88b56c057bdb5d058cd619d47bdd4.png" alt="$ \left( \prod_{j \in N \left( i \right)} \mathfrak{F} \left( U_j \right) ; \prod_{j \in N \left( i \right)} \mathfrak{P} \left( U_j \right) \right) $" />. Let <img class="teximage" src="/files/tex/76c7b422c8e228780f70a4f31614cfcf3f831c65.png" alt="$ H $" /> is a graph-composition of <img class="teximage" src="/files/tex/bfff269cc7df9bdb7c57d8b6a2a74020d114f24d.png" alt="$ F $" /> (regarding some partition <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> and external set <img class="teximage" src="/files/tex/b85ee8eb04b7b36a6f05b7f6218bef305019f707.png" alt="$ Z $" />). Then there exist a multifuncoid <img class="teximage" src="/files/tex/cc23d2b0c281befd62457dcbedbf9385be2cd2f6.png" alt="$ h $" /> of the form <img class="teximage" src="/files/tex/df5585afb153a7713c3b972518a8808361951cf0.png" alt="$ \lambda j \in Z : \mathfrak{P} \left( U_j \right) $" /> such that <img class="teximage" src="/files/tex/58f97b913328b408982a64ecf4dd15fda6ad2df8.png" alt="$ H = E^{\ast} h $" /> regarding the filtrator <img class="teximage" src="/files/tex/5a6d012c147b71bceeaa2eb8bf011efb3caa8ca5.png" alt="$ \left( \prod_{j \in Z} \mathfrak{F} \left( U_j \right) ; \prod_{j \in Z} \mathfrak{P} \left( U_j \right) \right) $" />. </div> </tr></td> </table> </td> </tr> </table> Porton, Victor graph-product multifuncoid Topology http://openproblemgarden.org/op/graph_product_of_multifuncoids#comment Sun, 12 Feb 2012 19:19:39 +0100 porton 37389 at http://openproblemgarden.org