All 8. Let (X, d) be a metric space, and A, B are subset of X, then(i) Fr(A) = A n (A)° = Ã – int AA - int A%D(ii) Fr(A) = 0 if and only if A is both open and closed%3D(iii) A is closed if and only if A Fr(A)ini(A mi)(iv) A is open if and only if A° 2 Fr(A)(v) Fr(AnB) C Fr(A) U Fr(B). The equality holds if A N B = ¢(vi) Fr(int A) C Fr(A).%3Dbas amonoori mort wollo

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....

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8. Let (X, d) be a metric space, and A, B are subset of X, the. (i) Fr(A) = A O (A)° = A - int A (ii) Fr(A) = 0 if and only if A is both open and closed (iii) A is closed if and only if A Fr(A)