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January 24, 2022 10:32 am 30 pts
Which one of the following spaces, with the usual metric, is not separable? rQuestion ID = 21471 1he space C[a, b] of the set of all real valued continuous functions defined on [a, b]. Option ID 1 8586) he space l of all bounded real sequences with supremum metric. [Option 1D 8588] The Euclidean space R". [Option ID = 8585] The space l of all absolutely convergent real sequences. [Option ID = 8587] 4. Correct Answer : The space of all bounded real sequences with supremum metric. [Option ID 8588] oLet G be an abelian group of order 2018 and f: G G be defined as fx) = x*. Then 8) [Question ID = 2118] fis not injective. [option ID 8470] fis not surjective [Option ID = 8471] there exists e # x E G such that flr) = x Option ID = 8472] fis an automorphism or G. rOption ID 8469] Correct Answer:- fis an automorphism of G. [Option ID = 8469]] If f:R>R is a continuous function such that fx + y) =fx) + fy), for all x, y e R, then [Question ID = 2138] , fis increasing if f(1) 20 and decreasing if f(1) s 0. [Option ID = 8551] f is increasing if f(1) <0 and decreasing if f(1) > 0. 2. [Option 1D 8552] fis a not an increasing function. [Option 1D= 8549] 3. fis neither an increasing nor a decreasing function. 4. [Option ID = 8550 Correct Answer:- fis increasing if f(1) 20 and decreasing if f(1) s 0. [Option ID = 8551] 10) r
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