Definition:Ordered Sum/General Definition

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Definition

Let $S_1, S_2, \ldots, S_n$ be tosets.

Then we define $T_n$ as the ordered sum of $S_1, S_2, \ldots, S_n$ as:

$\forall n \in \N_{>0}: T_n = \begin {cases}

S_1 & : n = 1 \\ T_{n - 1} + S_n & : n > 1 \end {cases}$

Also see

• Ordered Sum of Tosets is Totally Ordered Set: General Result

Sources

• 1968: A.N. Kolmogorov and S.V. Fomin: Introductory Real Analysis ... (previous) ... (next): $\S 3.4$: Ordered sums and products of ordered sets