Exercise 6. Consider the metric space (X, d) = (R, | - |). For each of the following subsets of R decide if they are open, closed, or not open and not closed, connected or not connected. Also, in each case write down the set of accumulation points.Justify your answers. \text { 1) } A=0 \text { 2) } A=0 \cap[0,1] \text {. } \text { 3) } A=\left\{(-1)^{n}\left(1+\frac{1}{n}\right)\right\} \text {. } \text { 4) } A=\bigcup_{n \in N}\left[n, n+\frac{1}{n}\right] \text { 5) } A=\bigcup_{n \in N}\left[\frac{1}{2^{m+1}}, \frac{1}{2^{n}}\right]

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