If $p$ and $q $ are two prime ideals of a commutative ring $R $ such that $p \subseteq q$, then we can esaeily define a continuous function (a path) $f$ from the unite interval $ [0,1]$ to the prime spectrume $ Spec (R)$, with the Zariski topology, such that $f (0)=p$ and $f (1)=q$. (Also, in general, if there exists a zigzag of specilization of prime ideals between $p $ and $q $, then we can find a path between $p $ and $q $). Now if there exists no zigzag of specilization of prime ideals between $p $ and $q $, I am looking for some conditions (on $p $ and $q$) under which there exists a path between $ p$ and $q $.

If $p$ and $q $ are two prime ideals of a commutative ring $R $ such that $p \subseteq q$, then we can easily define a continuous function (a path) $f$ from the unit interval $ [0,1]$ to the prime spectrum $ Spec (R)$, with the Zariski topology, such that $f (0)=p$ and $f (1)=q$. (Also, in general, if there exists a zigzag of specializations of prime ideals between $p $ and $q $, then we can find a path between $p $ and $q $). Now if there exists no zigzag of specializations of prime ideals between $p $ and $q $, I am looking for some conditions (on $p $ and $q$) under which there exists a path between $ p$ and $q $.