While the "Unity of Place" was simply the necessity of construction for the Greek stage, the only unity that Aristotle insisted upon was the "Unity of Action" although he did state that tragedy must keep its action "within one revolution of the sun," implying that "Unity of Time" is also a requisite to tragedy.
Unity of Place
The action of Oedipus Rex by Sophocles centers around Thebes where the city has been beset with plagues, famines, and fire. As king, Oedipus promises to seek the reason for these punishments; in so doing, he learns that the gods have reacted against the murder of their previous king, Laius. And, tragically, it is revealed that Oedipus has been the murderer. Oedipus punishes himself by blinding himself; then, he has Creon order his exile. ending the play, however, with Oedipus being led into the palace.
Unity of Time
The plot of Oedipus Rex does keep its action within Aristotle's "one revolution of the sun." For, the incidents that lead to the tragedy-- the prophecy that causes Laius and Jocasta to give up their son, the discovery of the baby Oedipus, and the murder of Laius--are all outside the drama proper. It is only the attempt to learn the cause(s) of the problems in Thebes that concerns the drama.
Unity of Action
All the action of the drama proper revolves around the attempt of Oedipus to find a remedy for the terrible occurrences in Thebes. He sends his brother-in-law Creon to the Oracle of Apollo in Delphi to learn what causes the fire, famine, and plague in Thebes. When Creon returns, Oedipus begins his investigation of the death of his predecessor, Laius. Of course, he learns his own involvement in this death and the consequences of his actions.
In his Poetics, which has become the consummate guideline for tragedy, Aristotle praises Oedipus Rex for having an exemplary, well-constructed plot that takes place with one full day; in addition Aristotle contends that Sophocles's play is one which is capable of inspiring fear and pity not only in its audience but especially in those who have merely heard of the story. And, part of this impact upon audiences is due to the play's unity of action, as well as unified time and place.