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open_ball [2013/09/08 17:38] nikolaj created |
open_ball [2014/03/21 11:11] (current) |
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| ===== Open ball ===== | ===== Open ball ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $\langle d,X\rangle$ ... metric space | | + | | @#55CCEE: context | @#55CCEE: $\langle d,X\rangle$ ... metric space | |
| + | | @#55CCEE: context | @#55CCEE: $a\in X$ | | ||
| - | | @#FFBB00: $B:X\times \mathbb R_+^*\to \mathcal P(X)$ | | + | | @#FFBB00: definiendum | @#FFBB00: $B_a:\mathbb R_+^*\to \mathcal P(X)$ | |
| - | | @#FFBB00: $\langle r,a\rangle \mapsto B_a(r):= \{x\ |\ d(x,a)<r \}$ | | + | | @#FFBB00: definiendum | @#FFBB00: $B_a(r):= \{x\ |\ d(x,a)<r \}$ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
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| Wikipedia: [[http://en.wikipedia.org/wiki/Ball_%28mathematics%29|Ball (Mathematics)]] | Wikipedia: [[http://en.wikipedia.org/wiki/Ball_%28mathematics%29|Ball (Mathematics)]] | ||
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Requirements === | + | === Context === |
| [[Metric]] | [[Metric]] | ||
