8. Let (X, d) be a metric space, and A, B are subset o X, then (i) Fr(A) = A O (A)° = A – int A Avieo b (ii) Fr(A) = o 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 o X, then (i) Fr(A) = A O (A)° = A – int A Avieo b (ii) Fr(A) = o if and only if A is both open and closed (iii) A is closed if and only if A Fr(A)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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ASAP, Prove all the Subparts with handwriting solution.
Fr(A) is Frontier
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
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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