Gemara

(Beraisa): If a channel of water passes [through a Chatzer] under windows [of houses], one may lower a bucket and draw water from it only if it is less than three;

R. Shimon ben Gamliel permits if it is less than four.

(The channel itself is 10 deep and four wide. It is a Karmelis. It has banks below the Chatzer.) The Beraisa teaches that if the banks are narrow enough [they are Batel to the Reshuyos on each side, so] one may be Machlif (transfer from the Chatzer to the banks, and then to the channel).

Question: Rav Dimi said in the name of R. Yochanan that if a place is less than four by four, people of Reshus ha'Rabim or Reshus ha'Yachid may unload on it, as long as they do not use it to transfer [from one Reshus to the other].

Answer: R. Yochanan forbids transferring between Reshuyos mid'Oraisa. The Beraisa permits between Reshuyos mid'Rabanan.

Question: R. Yochanan forbids even Reshuyos mid'Rabanan!

(Rav): If a wall between two Chatzeros is 10 Tefachim tall and less than four Tefachim thick, neither may carry there at all;

(R. Yochanan): People from either Chatzer may bring food up and eat it [but they may not transfer].

This is like R. Yochanan taught elsewhere;

(Rav Dimi citing R. Yochanan): If a place is less than four by four, people of Reshus ha'Rabim or Reshus ha'Yachid may unload on it, as long as they do not use it to transfer.

Answer: Really, Ze'iri taught this last teaching [in the name of R. Yochanan].

Ze'iri holds that the Beraisa discusses the width of the channel. Tana'im argue about Rav Dimi's teaching (that less than four is not a Karmelis).

Question: The channel should be like Chorei (holes open to) Karmelis [which are like Karmelis]!

Answer #1 (Abaye bar Avin and R. Chanina bar Avin): Chorei Karmelis are not like Karmelis.

Answer #2 (Rav Ashi): Chorei Karmelis are like Karmelis only if they are close to the Karmelis. Here, the channel is far.

Answer #3 (to Question (j) - Ravina): The case is, there are walls on both banks where the channel enters and leaves [the Chatzer]. There is a gap between the walls;

Chachamim hold that a gap less than three is considered solid, due to Lavud. R. Shimon ben Gamliel applies Lavud to any gap less than four.

Shabbos 8b (Beraisa): Someone standing on a threshold may take from or give to a Ba'al ha'Bayis [in Reshus ha'Yachid], or take from or give to an Oni [in Reshus ha'Rabim].

The threshold is Mekom Petur, e.g. it is less than four by four. This is like Rav Dimi taught.

101a (Beraisa): One may not transfer from a ship to the sea or vice-versa;

R. Yehudah says, if the ship is 10 deep (it is Reshus ha'Yachid) but the deck is not 10 above the water, one may transfer from it to the sea, but not vice-versa.

R. Yehudah permits pouring on the side of the ship because it descends to the sea by itself. This shows that Ko'ach (impetus) is permitted regarding a Karmelis.

Rishonim

Rif (24b): Below (87a), we establish R. Yochanan's teaching to refer to Reshuyos mid'Oraisa, e.g. Reshus ha'Yachid and Reshus ha'Rabim. For Reshuyos mid'Rabanan, e.g. a wall between two Chatzeros that is 10 tall but less than four wide, one may adjust a load and transfer. This is the Halachah.

R. Yehonason (DH Aval): It seems that one may transfer or adjust a load only on a wall without a roof over it. One may not do so in holes in a tall wall that is Mekorah, i.e. between two houses, even if the hole is less than four by four. R. Yochanan permits bringing Kelim of the house onto a wall only if the wall has no roof over it at all. Alternatively, since it has a roof, it is considered full, and the house floor is even with the hole in the wall or the top of the wall, so it is as if it is four wide, therefore one may not adjust on it, and all the more so one may not transfer on it.

Rosh (8:8): R. Yochanan said [that one may not transfer] also regarding Reshuyos mid'Rabanan! If the wall between two Chatzeros is 10 tall and less than four wide, Rav said that no one may move the Peros at all. R. Yochanan permits people from either Chatzer to go up and eat them, but they may not transfer from one Chatzer to the other through the wall. We answer that Ze'iri taught that. The Rif concluded that one may transfer between Reshuyos mid'Rabanan. The Ba'al ha'Ma'or says that we rely on the answer of Rav Ashi (it seems that this should say "Ravina", like it says in Ba'al ha'Ma'or 29a - PF), who is Basra, and we need not rely on the weak answer that Ze'iri taught the latter teaching, and he distinguishes between Reshuyos mid'Oraisa and mid'Rabanan, unlike Rav Dimi. We find that Chachamim were more stringent about Reshuyos mid'Rabanan! Also on 101b we find that Chachamim forbid to transfer a key from Karmelis to Reshus ha'Yachid through Mekom Petur. The Gemara said this shows that the Halachah follows Rav Dimi, who forbids transferring between Reshuyos mid'Rabanan. Tosfos asked from our Sugya (which concludes unlike Rav Dimi), and said that Tana'im argue about Rav Dimi's law. This is a poor answer. The Ba'al ha'Ma'or's answer is primary. The Ra'avad holds like it.

Poskim

Shulchan Aruch (OC 346:1): Some forbid transferring between Reshuyos mid'Rabanan through Mekom Petur, and some permit.

Beis Yosef (DH v'Afilu): R. Yochanan forbids transferring between Reshuyos mid'Oraisa. The Beraisa permits between Reshuyos [for which the Isur to transfer between them is] mid'Rabanan (e.g. one of them is a Karmelis, or. both are Reshus ha'Yachid). The Rosh concluded like the Ba'al ha'Ma'or, that the Halachah follows R. Yochanan, like Rav Ashi's answer. The Magid Mishneh (15:20) says that the Rambam permits transferring between Reshuyos mid'Rabanan through Mekom Petur, and so rule the great authorities, but the Rashba rules like those who forbid.

Beis Yosef (DH v'Chasav): The Tur wrote Stam (that one may transfer Kelim through Mekom Petur. He did not distinguish between mid'Oraisa and mid'Rabanan), like the Rosh. He forbids "to take into the house." This implies that one may transfer Kelim that rested in the Chatzer (at the beginning of Shabbos) to the other Chatzer, for all Chatzeros are like one Reshus, like he wrote in Siman 372.

Kaf ha'Chayim (15): The Tur permits transferring Kelim that rested in the Chatzer even without Mekom Petur, since all Chatzeros are like one Reshus. The same applies to a Mekom Petur between a Reshus ha'Yachid and a Karmelis.

Gra (DH Yesh): The stringent opinion is like Ravina's answer, and R. Yochanan (76a, 101b).

Gra (DH v'Yesh): The lenient opinion is like the first answer, and R. Yochanan, Abaye, R. Chanina and Rav Ashi. They all hold like the first answer.

Mishnah Berurah (8,9): One opinion forbids also to take from Reshus ha'Yachid, rest it in Mekom Petur, and later take it from Mekom Petur and rest it in Karmelis. It holds that we do not distinguish mid'Oraisa for mid'Rabanan regarding this.

Mishnah Berurah (10): The latter opinion permits regarding Reshuyos mid'Rabanan, for we do not make a Gezeirah to guard a Gezeirah.

Bi'ur Halachah (DH bi'Reshuyos): At the end of this Siman, we say that if Mekom Petur is next to Karmelis, it becomes Karmelis. This is like the first opinion in the Rema 345:19. This opinion must hold that we discuss a Mekom Petur that is 10 tall (and less than four wide). All agree that it cannot be a Karmelis, for Karmelis does not extend above 10.

Kaf ha'Chayim (16): The lenient opinion permits transferring through Mekom Petur when it was Nach. Some say that it is even if it was not Nach, like 101a.

Note: I do not understand this. R. Yehudah permits only Ko'ach. This is why one may not take from the sea! The Eshel Avraham (355:11) says that only R. Yehudah permits. Tosfos (101a DH Rebbi) says that Rabanan forbid from Karmelis to Reshus ha'Yachid through Mekom Petur, i.e. even if it was not Nach!

Kaf ha'Chayim (16): Ma'amar Mordechai says that the Mechaber in Reish Siman 355, Magid Mishneh and Mordechai connote that it need not be Nach. The one who says that they argue about when it was not Nach holds that all permit when it was Nach.

Kaf ha'Chayim (17): The Birkei Yosef says that when the Mechaber says "some say... and some say...", he rules like the latter opinion. The Rema (372:6) rules like those who forbid. However, I wrote that l'Chatchilah the Mechaber is concerned for the first opinion. One should be stringent, but one may be lenient if it was Nach.