Word Count : 274

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To check if the collection \[ G' = \left\{ \left( \frac{1}{n+2}, \frac{1}{n} \right) : n \in \mathbb{N} \right\} \] is an open cover of the interval \( ]0, 1[ \), we need to confirm the following: 1. Openness of each set: We need to verify that each element of \( G' \), i.e., the ______ ______ ______ _______ _________ _______ ________ ________ ___ ______ ________ _______.
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_____ __________ __________ _____ ______ _____ __________.
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________ _______ ___ _________ _________ _____ _____ ____ ____.
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