Definition:Order Type

Definition

Let $\left({S, \preceq_1}\right)$ and $\left({T, \preceq_2}\right)$ be totally ordered sets.

Then $S$ and $T$ have the same (order) type if and only if they are order isomorphic.

Sources

• 1968: A.N. Kolmogorov and S.V. Fomin: Introductory Real Analysis ... (previous) ... (next): $\S 3.3$: Ordered sets. Order types
• 2000: James R. Munkres: Topology (2nd ed.) ... (previous) ... (next): $1$: Set Theory and Logic: $\S 3$: Relations