Q3/a/ If there exist an operation pp on P(X) satisfying1. CL(0) = 0A FUAMUAYEVA 22. AC CL(A) for any A = P(X)3. CI(CI(A)) = CL(A) for any A = P(X)4. Cl(AUB) = CL(A) U CL(B) for any A, B = P(X)Show that there exist a unique topology T on X such that p(A) = Cl(A) forany A = P(X)

Thus, we have shown that there exists a unique topology τ on X such that Cl(A)=CI(A) for any…

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Chapter3: Functions

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Q3/a/ If there exist an operation pp on P(X) satisfying
1. CL(0) = 0
A FUA
MUAYEVA 2
2. AC CL(A) for any A = P(X)
3. CI(CI(A)) = CL(A) for any A = P(X)
4. Cl(AUB) = CL(A) U CL(B) for any A, B = P(X)
Show that there exist a unique topology T on X such that p(A) = Cl(A) for
any A = P(X)

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Q3/a/ If there exist an operation pp on P(X) satisfying 1. CL(0) = 0 A FUA MUAYEVA 2 2. AC CL(A) for any A = P(X) 3. CI(CI(A)) = CL(A) for any A = P(X) 4. Cl(AUB) = CL(A) U CL(B) for any A, B = P(X) Show that there exist a unique topology T on X such that p(A) = Cl(A) for any A = P(X)