Changes

MyWikiBiz, Author Your Legacy — Monday November 04, 2024
Jump to navigationJump to search
Line 733: Line 733:  
Using the isomorphism between function spaces:
 
Using the isomorphism between function spaces:
   −
: ('''B'''<sup>''n''</sup>&nbsp;&times;&nbsp;'''D'''<sup>''n''</sup>&nbsp;&rarr;&nbsp;'''B''') &asymp; ('''B'''<sup>''n''</sup> &rarr; ('''D'''<sup>''n''</sup> &rarr; '''B''')),
+
: ('''B'''<sup>''n''</sup>&nbsp;&times;&nbsp;'''D'''<sup>''n''</sup>&nbsp;&rarr;&nbsp;'''B''') <math>\cong</math> ('''B'''<sup>''n''</sup> &rarr; ('''D'''<sup>''n''</sup> &rarr; '''B''')),
   −
each ''p'' : ''U''&prime' &rarr; '''B''' has a unique decomposition into a ''p''&prime; : '''B'''<sup>''n''</sup> &rarr; ('''D'''<sup>''n''</sup> &rarr; '''B''') and a set of ''p''&Prime; : '''D'''<sup>''n''</sup> &rarr; '''B''' such that:
+
each ''p'' : ''U''&prime; &rarr; '''B''' has a unique decomposition into a ''p''&prime; : '''B'''<sup>''n''</sup> &rarr; ('''D'''<sup>''n''</sup> &rarr; '''B''') and a set of ''p''&Prime; : '''D'''<sup>''n''</sup> &rarr; '''B''' such that:
   −
: ''p'' : '''B'''<sup>''n''</sup> &times; '''D'''<sup>''n''</sup> &rarr; '''B''' &asymp; ''p''&prime; : '''B'''<sup>''n''</sup> &rarr; ''p''&Prime; : ('''D'''<sup>''n''</sup> &rarr; '''B''').
+
: ''p'' : '''B'''<sup>''n''</sup> &times; '''D'''<sup>''n''</sup> &rarr; '''B''' <u>&asymp;</u> ''p''&prime; : '''B'''<sup>''n''</sup> &rarr; ''p''&Prime; : ('''D'''<sup>''n''</sup> &rarr; '''B''').
    
For the sake of the visual intuition we may imagine that each cell ''x'' in the diagram of ''U'' has springing from it the diagram of the proposition ''p''&prime;(''x'') = ''p''&Prime; in d''U''.
 
For the sake of the visual intuition we may imagine that each cell ''x'' in the diagram of ''U'' has springing from it the diagram of the proposition ''p''&prime;(''x'') = ''p''&Prime; in d''U''.
12,080

edits

Navigation menu