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Question: 123 given that proposition 1215 basic properties of open and...

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1.2.3 Given that: Proposition 1.2.15 (Basic properties of open and closed sets). Let (X, d) be a metric space. Prove the following (c) For any xo E X and r 〉 0, then the ball B(x0,r) is an open set. The set r E X : d(x, ro) K r is a closed set. (This set is sometimes called the closed ball of radius r centered at ro) And (e) If E is a subset of X, then E is open if and only if the complement X\E := {x E X : x 또 E} is closed.

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