(1) Determine if each of the following statements is true(T) or false(F). 1- In a metric space, every open ball is an open set. 2- For any set A in a metric space, An aA ¢ 3- Let X, Y are metric...

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Extracted text: (1) Determine if each of the following statements is true(T) or false(F). 1- In a metric space, every open ball is an open set. 2- For any set A in a metric space, An aA ¢ 3- Let X, Y are metric spaces and f : X →Y is continuous map then for any open set A in X, f(A) is open in Y. 4- For any closed subset A of a metric space, A' C A 5- In a metric space, the intersection of any family of open sets is open. 6- For any subset A of a metric space, (A°)° C A°. 7- In R with the usual metric, R+ has only one lower bound. 8- Let X, Y are metric spaces and f : X → Y .If for any A C X, f(A) C f(A) then f is continuous. 9- For any closed set A in a metric space, = A. 10- In any complete metric space, every Caushy sequence is convergent.