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  • REZA RANJBAR
    As you know Z (the set of all integer number)is a commutative ring With indentity. We difine L(p)={pk: k is integer number} such that p is prime number.
    Message 1 of 3 , Sep 4, 2004
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      As you know Z (the set of all integer number)is a commutative ring

      With indentity.

      We difine L(p)={pk: k is integer number} such that p is prime number.

      Now ,let X={L(p):p is a prime number}.

      For each subset E of Z,let W(E) denote the set of all L(p) in X which L(p) cotain E.



      Now, we have

      i)V(0)=X , V(Z)={}.

      ii)if (E(i))is any family of subsets of Z,then



      V(U E(i))=&V(E(i)). (U is union, & is intersection(cap)).





      V(E) U V(F)=V(E & F).



      These results show that the sets V(E) satisfy the axioms for closed

      Sets in a topological space .

      Nextly I will show property of this topology space.



      Saeed ranjbar.






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