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8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = A n (A)° = A – int A (ii) Fr(A) = o if and only if A is both open and closed %3D (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) = A n (A)° = A – int A (ii) Fr(A) = o if and only if A is both open and closed %3D (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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Fr(A), int(A) are standard notation
8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = A n (A)° = Ã – int A A - int A %3D (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) (A ni) (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). %3D
Transcribed Image Text:8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = A n (A)° = Ã – int A A - int A %3D (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) (A ni) (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). %3D
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