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half-open_subsets_of_ℝⁿ [2013/09/03 18:56] ben |
half-open_subsets_of_ℝⁿ [2014/03/21 11:11] (current) |
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| ===== Half-open subsets of ℝⁿ ===== | ===== Half-open subsets of ℝⁿ ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $p\in \mathbb N$ | | + | | @#55CCEE: context | @#55CCEE: $p\in \mathbb N$ | |
| - | | @#FFBB00: $\mathfrak J^p\equiv\{\ ]a,b]\ |\ a,b\in\mathbb R^p\ \land\ a\le b\}$ | | + | | @#FFBB00: definiendum | @#FFBB00: $\mathfrak J^p\equiv\{\ ]a,b]\ |\ a,b\in\mathbb R^p\ \land\ a\le b\}$ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| This set is one which generates the $\sigma$-Algebra $\mathcal B^p$ of Borel subset of $\mathbb R^p$. | This set is one which generates the $\sigma$-Algebra $\mathcal B^p$ of Borel subset of $\mathbb R^p$. | ||
| - | ==== Context ==== | + | |
| - | === Requirements === | + | We also write |
| + | |||
| + | | @#FFBB00: definiendum | @#FFBB00: $\mathfrak J\equiv \mathfrak J^1$ | | ||
| + | ==== Parents ==== | ||
| + | === Context === | ||
| [[Real coordinate space]] | [[Real coordinate space]] | ||
