http://openproblemgarden.org/op/decomposition_of_completions_of_reloids Comments for "Decomposition of completions of reloids" en http://openproblemgarden.org/op/decomposition_of_completions_of_reloids <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 composable reloids <img class="teximage" src="/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png" alt="$ f $" /> and <img class="teximage" src="/files/tex/4239ee4145983e1d8ad375f0606cc7140bce36a3.png" alt="$ g $" /> it holds<br /> <ol class="enumerate"> \item <img class="teximage" src="/files/tex/0844704618d467ae0507a89bdb4b215b28d57759.png" alt="$ \operatorname{Compl} ( g \circ f) = ( \operatorname{Compl} g) \circ f $" /> if <img class="teximage" src="/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png" alt="$ f $" /> is a co-complete reloid; \item <img class="teximage" src="/files/tex/91a46d5da19358329c8cdb7351eae9cdb03c2764.png" alt="$ \operatorname{CoCompl} ( f \circ g) = f \circ \operatorname{CoCompl} g $" /> if <img class="teximage" src="/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png" alt="$ f $" /> is a complete reloid; \item <img class="teximage" src="/files/tex/92e3ac66e1ae6505f78e9f443665d1bcb234fe13.png" alt="$ \operatorname{CoCompl} ( ( \operatorname{Compl} g) \circ f) = \operatorname{Compl} ( g \circ ( \operatorname{CoCompl} f)) = ( \operatorname{Compl} g) \circ ( \operatorname{CoCompl} f) $" />; \item <img class="teximage" src="/files/tex/528dc0c7455fad4558f8b970c989e96990663021.png" alt="$ \operatorname{Compl} ( g \circ ( \operatorname{Compl} f)) = \operatorname{Compl} ( g \circ f) $" />; \item <img class="teximage" src="/files/tex/61a4422f23782d6433a39d5ed6a48dd554f3d16f.png" alt="$ \operatorname{CoCompl} ( ( \operatorname{CoCompl} g) \circ f) = \operatorname{CoCompl} ( g \circ f) $" />. </ol> </div> </tr></td> </table> </td> </tr> </table> Porton, Victor co-completion completion reloid Topology http://openproblemgarden.org/op/decomposition_of_completions_of_reloids#comment Mon, 02 Sep 2013 18:10:59 +0200 porton 56573 at http://openproblemgarden.org