= Solution
A <Suslin line> is a <dense linear order without endpoints> that is <order-complete>, has the <countable chain condition for a linear order>, and is not separable in its <order topology>. Thus every disjoint family of nonempty open intervals is countable, but there is no countable <order-dense subset>. The completeness condition says that every nonempty bounded-above subset has a <supremum>. These requirements distinguish a <Suslin line> from the real line, which has the countable <order-dense subset> $\mathbb Q$.
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