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) = ¢ if and only if A is both open and closed (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) = ¢ if and only if A is both open and closed (iii) A is closed if and only if A Fr(A)
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
(i) Fr(A) = A n (A)° = Ã – int A
A - 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).
%3D
bas amonoori mort wollo](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F167b2585-d12c-48f9-800c-0de8f67e18ee%2Fa10828e8-c0c8-4897-9b20-ebd8b28d4002%2F5nuacva_processed.jpeg&w=3840&q=75)
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
%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).
%3D
bas amonoori mort wollo
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