Before us is chapter 9 of Maseches Eruvin, mishnah 1. This mishnah discusses the relationship between the various areas found throughout a city - the houses, the courtyards, the roofs and the open spaces - and whether one may carry from one area to another.
The mishnah opens by ruling: "Kol gagos ha'ir reshus achas" - all the roofs of the city are considered one domain, a single area, and one may carry from roof to roof, even though beneath each and every roof there is a different house.
The opinion of Rabbi Meir:
As will become clear, this is the opinion of Rabbi Meir, who holds that since roofs are not in regular use, the law of the division of domains does not apply to them - we do not say that they are clearly divided among different owners.
Therefore their law is like that of a courtyard: vessels that were in the courtyard when Shabbos began may be carried within the courtyard, but the vessels that are in the houses of the courtyard may not be brought out into it. Those vessels that rested in the courtyard for the whole of Shabbos may be carried. And the same law applies among the roofs as well: one may carry from one roof to another, so long as one does not bring the vessels of the house out onto the roof.
"Uvilvad shelo yehei gag gavoha asarah o namuch asarah - divrei Rabbi Meir":
Rabbi Meir adds one qualification: the permission to carry applies on condition that no roof is ten handbreadths higher than its neighbor or ten handbreadths lower than it. This qualification is a decree made out of concern for a mistake, for if there is a difference of ten handbreadths between the heights - even though all the roofs are a private domain - an onlooker is liable to compare this to a post or a ledge standing in a public domain, whose height is ten handbreadths and whose width is four by four handbreadths, and whose status is that of a private domain. Someone who sees a person carrying between roofs of equal height is liable to think that it is permitted to carry even from the post into the public domain below, or the reverse, without understanding that there is a fundamental difference between the two cases: with roofs, everything is a private domain, unlike a post that stands in a public domain and whose status is that of a private domain. Because of this concern, when such a difference in height exists between the roofs, one may not carry from one to the other; but with less than that, carrying is permitted.
The opinion of the Sages:
And the Sages say: "Kol echad ve'echad reshus bifnei atzmo". The Sages disagree and hold that just as beneath each and every roof there is a separate house, so too the roofs themselves are separate domains and separate areas, and one may not carry from one to the other - unless, of course, an eruv was made between them. The discussion here is where there is no permission granted by an eruv.
The opinion of Rabbi Shimon:
Rabbi Shimon says: "Echad gagos ve'echad chatzeiros ve'echad karpeifos" - the roofs of the city, its courtyards and the karpeifos are all one domain and are considered a single area. The three areas are:
Gagos - the roofs of the city's houses.
Chatzeiros - the courtyards of the city.
Karpeifos - large back areas used for storing wood and the like, provided that the open space is not larger than a beis se'asayim, that is, the area in which two se'ah of grain can be sown, the size of the courtyard of the Mishkan.
However, this permission was stated specifically regarding vessels that rested within them - vessels that spent Shabbos in those areas - and not regarding vessels that began Shabbos inside the house. Vessels that were in the house when Shabbos began, even if they were brought out into the courtyard by virtue of an eruv, may not be carried from courtyard to courtyard or from the courtyard to a roof and the like, since their status is that of "vessels of the house" that entered Shabbos in the house.
In summary: in this mishnah the Tannaim disagree about the relationship between the areas of the city. According to Rabbi Meir all the roofs of the city are one domain, because the division of domains does not apply to them, and one may carry between them the vessels that rested there - provided that there is no difference of ten handbreadths in height between the roofs, out of concern that a person will err and derive from this a permission to carry from a post in the public domain and the reverse. The Sages hold that each roof is a domain of its own, like each house beneath it. And Rabbi Shimon expands the ruling and holds that the roofs, the courtyards and the karpeifos that are not larger than a beis se'asayim are all one domain, but this applies only to vessels that rested within them, and not to vessels that rested in the house.