1) THE STATUS OF AN UNENCLOSED ROOF
OPINIONS: Rav rules that when many roofs adjoin each other, one is permitted to carry through all of them on Shabbos. The Gemara questions this ruling from another statement of Rav. In the Gemara earlier, (89a) Rav says that one may not carry on the roof because the Mechitzos below are not considered to rise up and surround the roof. The Gemara answers that in this case, the outer wall of the building is recognizable and thus is considered to rise up and surround the roof. Since the roof does not overhang the side of the building, and the end of the roof is flush with the building's outer wall, the Mechitzah of the outer wall is considered to rise and surround the roof.
Why would it have been forbidden to carry on the roof if the outer wall of the building would not have been considered a valid Mechitzah for the roof?
(a) RASHI (DH Kasha) explains that it would have been forbidden to carry on the roof because of the people in Reshus ha'Rabim who are right next to the roof. If the roof has no Mechitzah and it borders Reshus ha'Rabim, the roof is "Parutz b'Milu'ah" to Reshus ha'Rabim, and thus one is forbidden to carry on the roof just as one is forbidden to carry in Reshus ha'Rabim.
(b) TOSFOS (beginning of 89b) writes that any area that is four by four Tefachim and is not enclosed by valid Mechitzos has the status of a Karmelis. The Reshus ha'Rabim outside the roof has no effect on the roof, since it is ten Tefachim or more below the roof. Rather, since the roof has no Mechitzah and its dimensions are at least four by four Tefachim, it is defined as a Karmelis in which it is prohibited to carry.
(c) Tosfos suggests further that perhaps the Gemara assumes that the roof should be considered a Karmelis because it is more than a Beis Se'asayim in size and was not Hukaf l'Dirah. (Even though the Gemara introduces this factor only in its answer to the contradiction between the statements of Shmuel, it is possible that the Gemara, when it questions Rav's ruling, already assumes that the area of the roofs is greater than a Beis Se'asayim. When the Gemara questions Shmuel's ruling, it assumes that Shmuel maintains that the principle of Gud Asik (which enables us to view the walls as extending upwards) would not only give the roof a Mechitzah but would also make it Hukaf l'Dirah. The Gemara answers that the principle of Gud Asik is not able to make an area Hukaf l'Dirah according to Shmuel.)
2) WHAT DOES AN ERUV ACCOMPLISH?
QUESTION: Rav Yehudah says that according to Rebbi Meir, all adjacent roofs are considered one domain (and one may carry from one roof to another), all adjacent Chatzeros are considered one domain, and all Karpifos are considered one domain. According to the Chachamim, roofs and Chatzeros together are considered one domain (and one may carry from a roof to a Chatzer), and all Karpifos are considered one domain. According to Rebbi Shimon, all three are considered one domain.
RASHI on the Mishnah (89a, DH Rebbi Shimon) writes that according to Rebbi Shimon, an Eruv Chatzeros is needed only in order to permit one to carry utensils from the house to the Chatzer, since one is permitted to move items between two Chatzeros (and roofs and Karpifos) even without an Eruv. Rashi's emphasis on why an Eruv is needed only according to Rebbi Shimon implies that according to Rebbi Meir and the Chachamim, it is obvious that an Eruv Chatzeros is necessary.
Why is this obvious? Since they maintain that all adjacent Chatzeros are considered one domain, why do they require an Eruv between two Chatzeros? It must be that they require an Eruv for the same reason that Rebbi Shimon does -- to permit one to carry utensils from the house to the Chatzer. Why, then, does Rashi give this reason only when he explains the view of Rebbi Shimon?
ANSWER: RASHI (end of 90b, DH v'Chatzeros) writes that Rebbi Meir's statement that adjacent Chatzeros are considered one domain applies only with regard to one who carries from a Chatzer Shel Rabim (a public Chatzer into which a number of private homes open) to another Chatzer Shel Rabim. According to Rashi, Rebbi Meir prohibits one from carrying from a Chatzer Shel Yachid (a privately-owned Chatzer) to a Chatzer Shel Rabim. The same applies to the opinion of the Chachamim. In order to permit one to carry from a private Chatzer to a public Chatzer, Rebbi Meir and the Chachamim maintain that an Eruv Chatzeros between the two Chatzeros is necessary. Rebbi Shimon, though, maintains that one is permitted to carry from any type of Chatzer to any other type of Chatzer, and an Eruv is never necessary to permit carrying from one Chatzer to another.
This is evident from the Gemara later (91a), where the Gemara says that according to the Chachamim one is prohibited from carrying from a Chatzer to a Mavoy. This is because a Chatzer compared to a Mavoy is like a private Chatzer compared to a public one (since the Mavoy is owned by many Chatzeros). (M. KORNFELD)