The Eleatics were monists, and their most famous pupil was the great paradoxist Zeno whose is most well known for the famous race between Achilles and the tortoise. The result of the race is less important than Zeno's technique which Aristotle called "dialectic syllogism" but in modern terms is known as reductio ad absurdem. He also uses the rather modern method of systematic assumption, which pervades Wittgenstein as well as Hofstadter, and Russell.
Parmenides and Melissus were both of the Eleatic school of monism which stipulated that all things are one, but it lacks the intellectual fortitude of Heraclitus and the Taoist tradition, neglecting the plenitude of particulars that define our experience of this world. It was our experience, our seeming, they argue that was the illusion, and the logical consequences of such a system are refuted by modern physics and are thus of little consequence.
Suffice it to say, they believe that the Great One was unchanging and uncreated, and thus everlasting. Space was boundless, and filled. Reality was eternal, unlimited, everywhere alike, unchanging, unchangeable, and pervasively filled.
This incomplete doctrine of the Monists would lead to another which fulfilled it. Namely the doctrine of Qualitative Pluralism.