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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.
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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