Word Count : 436

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Let's analyze each statement carefully: ### (a) The outer measure \( m^* \) of the set \( A = \{x \in \mathbb{R} : x^2 = 1\} \cup \{-3,2\} \) is 0. The set \( A \) consists of the points \( \{-1,1,-3,2\} \), which is a finite set. The Lebesgue outer measure \( m^* \) of any finite or countable set in \( \mathbb{R} \) is 0. ✅ True. ### (b) A finite subset of a metric space is totally bounded. A subset \( S \) of a metric space is totally bounded if, for every \( \epsilon > 0 \), there exists a finite cover of \( S ________ ___ ______ _______ _____ ________ ____ _____ __________ _______ _______.
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