[See Steps] Show that \mathcalB is generated by each of the following: The open intervals \mathcalE_1=(a, b):
Question: Show that \(\mathcal{B}\) is generated by each of the following:
- The open intervals \(\mathcal{E}_{1}=\{(a, b): a<b\}\).
- The closed intervals \(\mathcal{E}_{2}=\{[a, b]: a<b\}\).
- The half-open intervals \(\mathcal{E}_{3}=\{(a, b],[a, b): a<b\}\).
- The open rays \(\mathcal{E}_{4}=\{(a, \infty),(-\infty, b): a, b \in \mathbb{R}\}\).
- The closed rays \(\mathcal{E}_{5}=\{[a, \infty),(-\infty, b]: a, b \in \mathbb{R}\}\).
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