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Akash Babu posted an Question
July 10, 2022 • 21:42 pm 30 points
• CSIR NET
• Mathematical Sciences

A metric space (x, d) consists of a non-empty set x and a tunctiond:x*x-[0,) sucd h that 1. (positivity) for all x, y.e x, d{x, y) 2 with equality if and only i

A metric space (X, d) consists of a non-empty set X and a tunctiond:X*X-[0,) sucd h that 1. (Positivity) For all x, y.e X, d{x, y) 2 with equality if and only if x = y. (Symmetry) For all x, y e X, d(x.y) = d(yx). (Triangle Inequality) For all x, y, z e X, dx, y) s dx, 2) + d(z, y) A function d satisfying conditions (i)-(in), is called a metric on X. Let A be a subset of (M,d), then which of the following are TRUE ? (A) A=N\G;AcC and C is open (B) A NiCAcCand C is closed (D) A A if and only if A is closed (C) A A if and only if A is open

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• Navdeep goyal 1

closure of a set A in a matrix space is intersection of closed set which contains A so options B correct A is closed iff A =A- so D also correct

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