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1)

(a) Rebbi Meir permits carrying from one roof-top to another - provided the one is not ten Tefachim taller than the other.

(b) The ownership of the one does not disturb the other owner from carrying from one roof-top to the other - because people do not tend to use the roofs that much.

(c) The Rabbanan hold - that each roof-top is a separate Reshus, so that, unless they make an Eruv, each one forbids the other one from carrying.

(d) According to Rebbi Shimon - roofs, courtyards and enclosures are all considered to be one Reshus for vessels that rested in the courtyard, though not for vessels that rested in the house.

(a) According to Rebbi Shimon - an Eruv combining the Chatzeros is necessary for vessels that were carried from the house to the Chatzer (by means of an Eruv Chatzeros).

(b) Rebbi Meir forbids carrying from one roof to another which is ten Tefachim higher than it - because of the similarity to a pile in the Reshus ha'Rabim, for which he decrees every similar case (even a ten Tefachim tall pillar in the Reshus ha'Yachid).

(a) Rebbi Meir's decree is confined to a pile, a mound and a pillar, to things that are *permanently fixed* there - but not to things like a mortar, a mill or a barrel, which are *not*.

(b) It is possible to carry from one Chatzer to another via a Pesach (but it is not permitted via the wall of the Chatzer).

(a) Rav restricts carrying on the roof (according to the Chachamim) to four Amos - because, since each roof is considered a separate Reshus, we apply the principle that when one Reshus opens completely into another, the one forbids the other to carry.

(b) Shmuel permits carrying even more than four Amos from one to the other.

(c) The Machlokes Rav and Shmuel speaks when the roofs are close together, in such a way that one cannot see the division between the walls. Otherwise (if the divisions between the houses are clearly visible), even Rav will agree that we say 'Gud Aseik Mechitzasah', and this will serve to divide all the roofs. (Note: Shmuel holds 'Gud Aseik Mechitzasah even through the roof) See also note in 5b.

(d) Rav will learn our Mishnah ('va'Chachamim Omrim, Kol Echad ve'Echad Reshus Le'atzmo') - not to permit carrying on the entire roof, but to forbid carrying from one roof to the other, even if it is less than four Tefachim.

5)

(a) Shmuel comments on the Mishnah 'Gag Gadol, Samuch le'Katan, ha'Gadol Mutar, ve'ha'Katan Asur' - 'Lo Shanu Ela she'Yesh Diyurin al Zeh, ve'Diyurin al Zeh, de'Havya Lah Ha de'Katan Mechitzah Nidreses, Aval Ein Diyurin al Zeh ve'Al Zeh, Sheneihem Mutarin' (because of 'Gud Aseik Mechatzasah').

(b) If the walls of the houses concerned were not very close, people would not walk across from one to the other, and Shmuel would not have called it 'a Mechitzah Nidreses'. (Note: It seems from here, that the walls have to be well apart before the break between the walls is called visible, and Rav will agree that we say 'Gud Aseik Mechitzasah' - though it is unclear as to why this should be so).

(c) What Rav Yosef claimed to have taught his Talmidim was 'Lo Shanu Ela she'Yesh Mechitzah al Zeh, u'Mechitzah al Zeh, de'Gadol Mishteri be'Gifufi, ve'Katan Nifratz be'Milu'o, Aval Ein Mechitzah Lo al Zeh ve'Lo al Zeh, Sheneihem Asurim'.

(d) When Abaye insisted that he had taught them something about 'Diyurin' - he amended that to 'Lo Shanu Ela she'Yesh Mechitzah Re'uyah le'Dirah al Zeh, u'Mechitzah Mechitzah Re'uyah le'Dirah al Zeh, de'Gadol Mishteri be'Gifufi, ve'Katan Nifratz be'Milu'o, Aval Yesh Mechitzah Re'uyah al ha'Gadol ve'Ein Re'uyah le'Dirah al ha'Katan, Sheneihem Asurim'. 'Mechitzah Re'uyah means a Mechtzah that is firmly fixed and is there to stay.

7)

(a) Abaye says that someone who builds another floor on his roof, with a Dakah of four Tefachim leading to the next roof is permitted to carry on all the roofs, for exactly the same reason as Rav Nachman permitted this by a fixed ladder.

(b) If he were to build a Dakah on the opposite side of his roof, facing his garden, then he would be forbidden to carry on all the roofs - because it is clear that he built it in order to keep an eye on his garden, and had withdrawn from the series of roofs (even according to Rebbi Meir, who normally considers all the roofs as one).