Taharos, Chapter 6, Mishnah 9. Our chapter deals with sfeikos and reshuyos: doubtful tumah, and how we decide whether a given place is a reshus harabbim or a reshus hayachid. One of the chapter's lessons is that these labels are not absolute. The very same structure can be a reshus hayachid when we are discussing the laws of Shabbos and a reshus harabbim when we are discussing tumah and taharah, because each body of halachah is asking its own question about the space.
Once again the mishnah takes us on a tour of Greek architecture.
The paran
The mishnah speaks of the "paran," the forum. This is a large public building, much like the great assembly hall discussed nearby, with two doorways set opposite one another. What sets it apart is that it also contains "tzaddin," side rooms off to the sides, and those side rooms are where the discussion in this mishnah lies.
The main structure itself is classified exactly as we would expect: "reshus hayachid l'Shabbos, reshus harabbim l'tumah." For Shabbos it counts as a private domain, since it is an enclosed building with a single owner. For tumah and taharah it is a public domain, since the public fills it.
The side rooms
Now comes the point of the mishnah: "v'chein hatzaddin," and so too the side rooms. According to the first opinion, presumably the view of the chachamim, the tzaddin carry no independent status. They are treated exactly like the rest of the forum, which means that for tumah and taharah they too are a reshus harabbim.
Rabbi Meir holds otherwise: "hatzaddin reshus hayachid lechach ulechach," the side rooms are a reshus hayachid for this and for that, meaning in both areas of halachah alike. To his mind these chambers are truly private no matter which angle you take, perhaps because entry to them is restricted rather than free to all comers, perhaps because of the arrangement of the facing doorways, or perhaps simply because the throngs never wander inside them. Whatever the reasoning, Rabbi Meir holds that they keep the standing of a private domain.
The halachah
And should you find yourself wandering through ancient Greece and step into the tzaddin of a forum, you may rest easy: we do not rule like Rabbi Meir. The side rooms share the status of the forum itself, a reshus hayachid for Shabbos and a reshus harabbim for tumah and taharah.