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 half-open_subsets_of_ℝⁿ [2013/09/05 01:19]nikolaj half-open_subsets_of_ℝⁿ [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2013/09/05 01:19 nikolaj 2013/09/05 01:19 nikolaj 2013/09/03 18:56 ben 2013/09/03 18:55 ben 2013/09/03 18:52 ben created Next revision Previous revision 2013/09/05 01:19 nikolaj 2013/09/05 01:19 nikolaj 2013/09/03 18:56 ben 2013/09/03 18:55 ben 2013/09/03 18:52 ben created Line 1: Line 1: ===== 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 $\mathbb R^p$. - | @#FFBB00: $\mathfrak J\equiv \mathfrak J^1$ | + We also write - ==== Context ​==== + - === Requirements ​=== + | @#FFBB00: definiendum ​| @#FFBB00: $\mathfrak J\equiv \mathfrak J^1$ | + ==== Parents ​==== + === Context ​=== [[Real coordinate space]] [[Real coordinate space]]