topologia de conjunts

Definició:


Si ( x€E & y€E ) ==> ( x [M] y )€E
Si ( x€E & y€E ) ==> ( x [W] y )€E


Si ( ¬x€E & ¬y€E ) ==> ( ¬x [M] ¬y )€E
Si ( ¬x€E & ¬y€E ) ==> ( ¬x [W] ¬y )€E


Teoremes:


¬( x [M] y )€E
¬( x [W] y )€E


¬( ¬x [M] ¬y )€E
¬( ¬x [W] ¬y )€E


Si ( x_{1}€E &...(n)...& x_{n}€E ) ==> ( x_{1} [M]...(n)...[M] x_{n} )€E
Si ( x_{1}€E &...(n)...& x_{n}€E ) ==> ( x_{1} [W]...(n)...[W] x_{n} )€E


Si ( ¬x_{1}€E &...(n)...& ¬x_{n}€E ) ==> ( ¬x_{1} [M]...(n)...[M] ¬x_{n} )€E
Si ( ¬x_{1}€E &...(n)...& ¬x_{n}€E ) ==> ( ¬x_{1} [W]...(n)...[W] ¬x_{n} )€E


¬( x_{1} [M]...(n)...[M] x_{n} )€E
¬( x_{1} [W]...(n)...[W] x_{n} )€E


¬( ¬x_{1} [M]...(n)...[M] ¬x_{n} )€E
¬( ¬x_{1} [W]...(n)...[W] ¬x_{n} )€E