Category:Definitions/Projections

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This category contains definitions related to Projections in the context of Mapping Theory.
Related results can be found in Category:Projections.


Let $S_1, S_2, \ldots, S_j, \ldots, S_n$ be sets.

Let $\displaystyle \prod_{i \mathop = 1}^n S_i$ be the Cartesian product of $S_1, S_2, \ldots, S_n$.

For each $j \in \set {1, 2, \ldots, n}$, the $j$th projection on $\displaystyle S = \prod_{i \mathop = 1}^n S_i$ is the mapping $\pr_j: S \to S_j$ defined by:

$\map {\pr_j} {s_1, s_2, \ldots, s_j, \ldots, s_n} = s_j$

for all $\tuple {s_1, s_2, \ldots, s_n} \in S$.