There are four classes of domains with regard to the laws of Shabbos: private domain, public domain, karmelis and makom petur. We shall explain them briefly.

What is a private domain? It is a place that is at least four tefachim¹ by four tefachim (which is sufficiently significant to be of use) and is surrounded by partitions² (345: 3)—Acharonim] at least ten tefachim high (even if the partitions are not complete). A trench, ten tefachim deep and four tefachim wide, has the same halachah as a partition.³ (345: 11). Similarly, the same is true of a hole⁴ (345: 10) See Mishnah Berurah (345: 41). If the water freezes, see Magein Avraham 363: 31 and Chayei Adam 47: 5. ten [tefachim] deep, and four tefachim by four tefachim wide, and also a mound ten tefachim high and four tefachim by four tefachim wide. Even a vessel such as a box, if it is ten [tefachim] high, or a round barrel that is large enough to circumscribe a four by four square; all of these, even if they are in a public domain or in a karmelis,⁵ are considered separate premises of their own and constitute a private domain. The open space over a private domain is considered a private domain until the sky.⁶ 7a. The tops of the walls that surround a private domain, are also considered a private domain. If there are holes in the walls on the side facing a private domain, even if they run through from side to side,⁷ 47: 7. since they can be used from the private domain, they are insignificant in comparison to the wall [and therefore] are considered as a private domain. (When the holes are only on the outside of the wall, this will be explained in the following paragraph.)

footnotes: ¹ See Glossary. ² The thickness of the walls is not included. [Mishnah Berurah ³ See Shulchan Aruch ⁴ The walls of a private domain have to be visible. If a hole is filled with water it is a private domain, but if it is filled with fruit, etc., it is not (even if you intend to remove the fruit). Magein Avraham ⁵ See footnote 12. ⁶ Maseches Shabbos ⁷ To a public domain. See Chayei Adam

What is a public domain? Streets and market squares that measure sixteen amos⁸ by sixteen amos are considered public domains, for this was the width of the road in the camp of the Levites in the desert.⁹ 99a. And highways by which people travel from city to city that are sixteen amos wide are [also] public domain. Anything in a public domain that is less than three tefachim above the ground, even thorns or dung on which most people do not step, is nevertheless insignificant when compared to the ground, and is considered part of a public domain.¹⁰ 7, Shulchan Aruch 345: 10–11. Likewise, a ditch in a public domain; that is less than three tefachim deep, is considered public domain. The holes in the walls facing a public domain that do not run through to a private domain, and are lower than three tefachim from the ground, are insignificant compared to the public domain, and are considered public domain. However, if they are higher than three tefachim [from the ground], we must consider them according to their dimensions.¹¹ 345: 13. If the hole measures four by four tefachim but is lower than ten tefachim, it is considered a karmelis;¹² is defined as an area which cannot be classified either as private or as public domain. See paragraph 4. if it is higher than ten tefachim, it is a private domain. If it is less than four by four tefachim it is a makom petur,¹³, as an exempted area. See paragraph 5. whether it is above ten tefachim or below ten tefachim [from the ground]. Alleys that lead into a public domain are sometimes regarded as public domain and sometimes as karmelis. This involves many intricate halachic details.¹⁴ 345: 8–9. Some authorities say,¹⁵ 345: 7 [Bahag, Rashi (Maseches Eruvin 6) Rosh, Smag etc.] that any place through which fewer than 600, 000 people¹⁶. [Maharsham Vol. 3, 188, Yeshuos Malka (Orach Chaim Resp. 26)] pass daily,¹⁷ (Maseches Eruvin 6b) and Eishel Avraham (Batchutch) 345—poskim.] as was the number of Jews in the desert,¹⁸. is not a public domain, but is regarded as a karmelis.¹⁹ Therefore, nowadays, we have no public domain.²⁰ Every God-fearing person should follow the more stringent view.²¹ etc. do not require that 600, 000 people pass by in order to make a public domain.

footnotes: ⁸ See Glossary. ⁹ See Maseches Shabbos ¹⁰ See Maseches Shabbos ¹¹ Shulchan Aruch ¹² Karmelis ¹³ Makom petur ¹⁴ See Shulchan Aruch ¹⁵ See Shulchan Aruch ¹⁶ Some say that this applies only to a city, but that major intercity highways are considered public domain even when there are not 600, 000 passers-by, even according to Rashi ¹⁷ Including non-Jews. [Beis Meir ¹⁸ During their forty years of wandering through the Sinai desert en route to Eretz Yisrael ¹⁹ See footnote 12. ²⁰ Almost none in the city, excluding large cities which are numerous nowadays. See footnotes 16 and 21. ²¹ The Rif, Rambam, Ramban, Rashba

What is a karmelis? It is any place that is not a public thoroughfare, and is not properly surrounded by partitions such as a field; or a stream that is no less than ten tefachim deep and no less than four tefachim wide; and alleys that have three²² 345: 14—Tur, Rambam. See Beis Yosef. partitions. Also an itztavanis, (which is a place in front of shops where merchants sit) or an itztaba, (a stand on which merchandise is placed,) in front of the pillars in the public domain, and [the itztaba] is four tefachim wide and from three tefachim to ten tefachim high. Also a place that measures four [tefachim] square, and is surrounded by partitions that are less than ten [tefachim] high; and a mound that measures four [tefachim] square and from three to ten [tefachim] high; and a pit that measures four [tefachim] square and is from three to ten [tefachim] deep. There are also many other examples of karmelis. (The word karmelis is a composite of rach and mol, which means, neither wet nor dry,²³ (Maseches Shabbos 6b). Also see Rashi (Maseches Shabbos 3b). but in between. The same applies in this case; it is neither a private domain, because it does not have proper walls, nor is it public domain, because not many walk there.)

footnotes: ²² Rema ²³ Tosafos

What is a mekom petur? It is any place in a public domain that does not measure four [tefachim] square and is more than three [tefachim] high; or a pit that is not four [tefachim] square and is deeper than three [tefachim] ; and a place that does not measure four [tefachim] square but is surrounded by partitions of three or more [tefachim] high.²⁴ 345: 19. All these places [are exempt] only when they are in a public domain, [for then] they are considered a mekom petur. But when they are in a karmelis, they are also considered part of karmelis.

footnotes: ²⁴ Shulchan Aruch