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indexed_union [2013/09/14 16:57] nikolaj |
indexed_union [2014/10/28 19:23] nikolaj |
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| ===== Indexed union ===== | ===== Indexed union ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $f:I\to X$ | | + | | @#55CCEE: context | @#55CCEE: $f:I\to X$ | |
| - | + | | @#FFBB00: definiendum | @#FFBB00: $\bigcup_{i\in I,\ f} X_i \equiv \bigcup \mathrm{im}(f)$ | | |
| - | | @#FFBB00: $\bigcup_{i\in I} X_i \equiv \bigcup \mathrm{im}(f)$ | | + | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| + | For $f=\mathrm{id}$, the set is indexing itself and the indexed union is just the arbitrary union $\bigcup_{i\in I} X_i = \bigcup X$. | ||
| ==== Parents ==== | ==== Parents ==== | ||
| === Refinement of === | === Refinement of === | ||
| [[Arbitrary union]] | [[Arbitrary union]] | ||
| - | === Requirements === | + | === Context === |
| [[Image]] | [[Image]] | ||
