Gemara

8a (Abaye): If one threw a basket that is 10 Tefachim tall [from Reshus ha'Yachid] to Reshus ha'Rabim, he is liable if its width (diameter) is less than six Tefachim wide, and liable if it is more than six, he is exempt. (Then, it itself is a Reshus ha'Yachid.)

99b - Question (Rav Meisha citing R. Yochanan): If there was a Karmelis in Reshus ha'Rabim, and one surrounded it with a wall 10 tall but less than four wide, making it Reshus ha'Yachid, and one threw onto the wall, what is the law?

Since it is not four wide, it is Mekom Petur;

Or, since it made a Reshus ha'Yachid, it is as if the interior is full [up to 10 Tefachim, so also the wall is Reshus ha'Yachid]?

Answer (Ula): Since it is a Mechitzah [by itself], and it makes something else Reshus ha'Yachid, all the more so it itself is Reshus ha'Yachid!

Eruvin 78a (Rav Huna): If a pillar in Reshus ha'Rabim is 10 tall and [exactly four by] four wide, and one inserted a peg of any thickness in the top, this diminishes [it. It is no longer Reshus ha'Yachid.]

(Abaye and Rava): The peg can even be less than three Tefachim tall.

This is because one cannot use its place.

(Rav Ashi): Even if it is three tall, it is not Mema'et.

This is because one can hang things from it.

Question (Rav Acha brei d'Rava): If one filled the entire top surface with pegs, what is the law?

Answer (Rav Ashi): We learn from R. Yochanan's law!

(R. Yochanan): A pit and its Chulyah (a ring of earth dug out from it) join towards 10 Tefachim to make Reshus ha'Yachid.

Question: Why do they join? One cannot use them together!

Answer: One can put a board or rock over the pit and use them together.

Summation of answer: Likewise, one can put a board over the pegs and use the area! (Therefore, it is not Mema'et.)

Rishonim

Rambam (Hilchos Shabbos 14:1): Reshus ha'Yachid is... any place surrounded by four walls 10 tall, and between them is at least four by four.

Rambam (2): Even Kelim, if there is in them four by four for a height of 10, they are a full Reshus ha'Yachid.

Rosh (1:4): Really, it suffices for the basket to be five and three fifths Tefachim. Abaye said six to distance people from Isur, but there is no Chiyuv Chatas when it is more than fifth and three fifths. The walls join with the interior [for four by four], just like the bottom joins towards 10.

Tosfos (8a DH Rechavah): R. Chananel says that we discuss a basket six wide, for each wall is a fifth of a Tefach thick, and we require air of four Tefachim in the basket. Even though it is 10 tall only with the thickness of the bottom, regarding the height it joins, for a ditch of five joins with a wall of five. I disagree. The thickness of a Chulyah joins with the hollow of the pit, for it is useful to put things on it, like it says in Eruvin.

Tosfos (Sukah 4b DH Pachos): If a five Tefachim wall was built on a mound five Tefachim tall, we should say that it is Reshus ha'Yachid, for one can put something on it and use it! I answer that we do not say so when it is very wide, e.g. 10 or 20 Amos. We say so only for something narrow, like a pillar four wide.

Poskim

Shulchan Aruch (OC 345:2): Reshus ha'Yachid is a place surrounded by walls 10 Tefachim tall and it has at least four by four Tefachim.

Bach (DH u'Mah): The Beis Yosef brings Rashi, who says that the Chalal (interior) is four. This connotes that it must be four excluding the thickness of the walls. Also the Rambam (14:1) connotes like this. He says "there is four by four between them." However, Tosfos and the Rosh hold that the thickness of the walls joins. The Tur agrees. Therefore, he did not write like the Rambam "between the walls." However, at the end of this Siman the Tur wrote "between the walls", which connotes that they do not join! This is difficult.

Taz (2): The Shulchan Aruch connotes that the thickness of the walls is measured with the interior to comprise four Tefachim. The Rosh and Tosfos explicitly say so for a basket, unlike the Rambam, who requires four inside the Kli. This is like Chulyas ha'Bor, which joins with the interior, since one can put something on the earth. Rashi says "we say Gud Asik on all four sides, so the top is surrounded on four sides and the hollow is four." Do not explain that the interior must be four without the walls. Rashi said Pnei (the face of) ha'Mechitzos, to teach that the outer edge goes up and becomes the Mechitzos. The thickness of the Mechitzos joins with the interior. Tosfos says that Rashi holds like Tosfos. The Rambam says 'they enclose four by four' to include the thickness of the walls. However, there is a difficulty. R. Yochanan asked about a Karmelis surrounded by walls 10 tall, but the walls are not four wide. Do we consider the area inside to be filled with earth? Ula answered was, since it makes the interior Reshus ha'Yachid, all the more so it itself is Reshus ha'Yachid! Rashi explains that the top is like an extension of the ground. Since the wall made Reshus ha'Yachid, it extends up to Shamayim. This implies that when the interior is Reshus ha'Yachid without the wall, it does not extend up to Shamayim, and it is not like an extension of the ground. Also, he concluded 'if it makes others Reshus ha'Yachid...' This is not clear here. This requires investigation.

Mishbetzos Zahav: The Mechaber wrote 'if there is in it', like the Tur, unlike the Rambam (14:1), who said 'between them is least four by four.' This connotes that the thickness of the walls joins towards four by four.

Note: In Halachah 2, the Rambam says 'if there is in them four by four'!

Mishbetzos Zahav: The Bach points out that the Tur himself wrote (below) 'if there is not between them'! The Taz says that the Rambam connotes that we include the thickness of the walls. If so, we can say that the Tur holds like the Rambam, and like the Mechaber in Sa'if 19. I say that the Taz agrees that within the walls is not Reshus ha'Yachid, since it is less than four by four and not useful. Above is Reshus ha'Yachid, for one can put a board on it and use the place. Tosfos says that R. Chananel holds that only a pillar four wide is Reshus ha'Yachid, for it is useful, but not if the interior is hollow. Or, perhaps a basket is different, for it is weak, of woven reeds, and one cannot put things on it. Tosfos (Sukah 4b) says that when it is very wide, one cannot put a board on it to put things on. Shabbos 99b connotes that if the walls do not make a Reshus ha'Yachid inside, they are not Reshus ha'Yachid. This is when the interior is not four by four below, the Taz agrees that even the top is not Reshus ha'Yachid. Perhaps this is why it discusses surrounding Karmelis. Rashi explains that he enclosed [less than] Beis Sa'atayim. However, it is at least 10 or 20 Amos, so one cannot put anything on it. If it is smaller, and useful, it is Reshus ha'Yachid even without the reason that it made the interior Reshus ha'Yachid.

Mishbetzos Zahav: When it is four by four only with the thickness of the walls, the top is Reshus ha'Yachid if the walls are strong. Tosfos asked why we needed to say that they enclosed Karmelis. The Mechaber (Sa'if 3) brought the law, but omitted the reason that it made the interior Reshus ha'Yachid. The Rambam (14:3) brought the reason to teach that the thickness of the walls does not join to four by four even at the top. The Mechaber omitted this, for he holds (Sa'if 2) that the thickness of the walls join.

Magen Avraham (1): In Sa'if, 19, the Shulchan Aruch requires that there be four Tefachim between the walls. This is unlike Olas Shabbos.

Mishnah Berurah (3): In Sa'if 19, we require a gap of four by four, excluding the thickness of the walls. Most Poskim hold like this. Some say that the thickness of the walls joins. Eliyahu Rabah brings from the Rashba [also Milchamos Hash-m says so] that Mechitzos join only if they are thick, and useful to put things on them. The Acharonim say that this only makes a Reshus ha'Yachid on top of the thickness of the walls, but all agree that the interior is Reshus ha'Yachid only if the gap is four by four.

Kaf ha'Chayim (9): The Taz was unsure whether or not the thickness of the walls joins. The Bach and Magen Avraham were sure that it does not join. Mor u'Ktzi'ah rejected this, for the Rishonim clearly hold that strong walls join, for one can use them through putting a board on them. Machazik Berachah says that the Shulchan Aruch holds like this. Sa'if 19 discusses weak walls. Chemdas Moshe says that using them makes the top of them Reshus ha'Yachid, but the interior is Reshus ha'Yachid, to be Mechayev one who transfers from it to Reshus ha'Rabim, only if the area within the walls is four by four by itself. Even ha'Ozer, Tosefes Shabbos, Mishbetzos Zahav and the Acharonim agree.

Shulchan Aruch (19): If Mechitzos are at least three Tefachim tall, but there is not between them four by four, the area is Mekom Petur.

Magen Avraham (16): The Shulchan Aruch connotes that the thickness of the walls does not join towards four by four.