For the source text click/tap here: Sukkah 19
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Can a sukkah be made without any roof at all?
This is the question debated in the Mishnah on our daf. According to the Mishnah, the Chachamim allow a sukkah that is built like a tzrif – a triangular shack, or one that is built leaning against a wall. Rabbi Eliezer rules that such sukkot are no good because they have no roof.
If one wants to use a reed mat for the covering of his sukkah - a very convenient way, rather than messing with the leaves and branches - will it be a kosher s'chach? - A small mat is made for lying down on it, and it is thus a utensil; since all utensils are susceptible to ritual impurity, and therefore cannot be used for the sukkah covering, the small mat is not kosher.
However, with large mats it depends. If it was made originally for lying down, it is a utensil and cannot be used; but if it was made for covering the sukkah - then it is not a utensil in the normal sense of the word, does not accept ritual impurity, and therefore is a kosher sukkah covering.
Rashi explains that a large mat of reeds is hard and rough, and it is generally not to be used for a bed. However, if it was specifically manufactured in order to be a bed, it has the status of being a כלי, and it is therefore eligible to become טמא. This mat cannot be used for סכך.
Shulchan Aruch rules that small mats may not be used for סכך unless they are made specifically for use as סכך since they are primarily used for sleeping.
Large mats, on the other hand, may be used for סכך, unless they are made specifically for sleeping, since they are primarily used for סכך. Rema (2) writes that if most people in town manufacture mats for sleeping one may not use a mat for סכך even if he made the mat specifically for סכך. The reason is that others may suspect that he is using for סכך a mat that is susceptible to tumah.