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8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = Ã~ (Ā)º = Ā – int A (ii) Fr(A) = ¢ if and only if A is both open and closed = A) vino b (iii) A is closed if and only if A Fr(A)

8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = Ã~ (Ā)º = Ā – int A (ii) Fr(A) = ¢ if and only if A is both open and closed = A) vino b (iii) A is closed if and only if A Fr(A)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8. Let (X, d) be a metric space, and A, B are subset of X, then bas (i) Fr(A) = A (A) = A - int A (ii) Fr(A) = if and only if A is both open and closed Ayo b ¢ (iii) A is closed if and only if A Fr(A) C (iv) A is open if and only if A Fr(A) (v) Fr(A^B) ≤ Fr(A) U Fr(B). The equality holds if Ã~ B = ¢ NG keres cs sds bas & emen bas famshoudt mod wollo (vi) Fr(int A) C Fr(A).
Transcribed Image Text:8. Let (X, d) be a metric space, and A, B are subset of X, then bas (i) Fr(A) = A (A) = A - int A (ii) Fr(A) = if and only if A is both open and closed Ayo b ¢ (iii) A is closed if and only if A Fr(A) C (iv) A is open if and only if A Fr(A) (v) Fr(A^B) ≤ Fr(A) U Fr(B). The equality holds if Ã~ B = ¢ NG keres cs sds bas & emen bas famshoudt mod wollo (vi) Fr(int A) C Fr(A).
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