A dense linear order is a Chains $\mathbf{D}=\langle D,\le\rangle$ such that

$\le$ is dense: $x<y\Longrightarrow\exists z (x<z$, $z<y)$

Remark:

Let $\mathbf{C}$ and $\mathbf{D}$ be dense linear orders. A morphism from $\mathbf{C}$ to $\mathbf{D}$ is a function $h:C\rightarrow D$ that is a orderpreserving:

$x\le y\Longrightarrow h(x)\le h(y)$

Example 1:

$\begin{array}{lr} None \end{array}$

Dense linear orders without endpoints

Chains