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I'm trying to find the correct term for a specific kind of totally ordered space:

Let $S$ be a totally ordered space with strict total order $<$.

Property: For any two $s_{1}$ and $s_{2}$ in $S$ where $s_1 < s_2$, there must exist some $s_{3}$ such that $s_{1} < s_{3}$ and $s_{3} < s_{2}$.

What is the name of this property? Thank you!

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closed as off-topic by Emil Jeřábek, Joseph Van Name, Christian Remling, Alex Degtyarev, Joonas Ilmavirta Apr 30 '15 at 6:36

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up vote 6 down vote accepted

Dense order is one name that concept goes by.

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Thank you so much, Mariano! – user1998 Dec 20 '09 at 1:37

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