  Let $T$ be a totally ordered set and let $D(T)$ denote the set of all cuts of
$T$. We prove the existence of a discrete valuation domain $O_{v}$ such that
$T$ is order isomorphic to two special subsets of Spec$(O_{v})$. We prove that
if $A$ is a ring (not necessarily commutative) whose prime spectrum is totally
ordered and satisfies (K2), then there exists a totally ordered set $U
\subseteq \text{Spec}(A)$ such that the prime spectrum of $A$ is order
isomorphic to $D(U)$. We also present equivalent conditions for a totally
ordered set to be a Dedekind totally ordered set. At the end, we present an
algebraic geometry point of view
