Eruvin 102B

בשיפועה טפח, אבל יש בשיפועה טפח ⁠— שיפועי אהלים כאהלים דמו.

its incline does not extend a handbreadth from the center to each side. However, if its incline extends a handbreadth from the center to the side, the halakha is that the inclines of tents are considered like tents, and it is therefore prohibited to suspend them.

ואמר רב שישא בריה דרב אידי: סיינא ⁠— שרי. והתניא אסור! לא קשיא: הא ⁠— דאית ביה טפח, הא ⁠— דלית ביה טפח.

And Rav Sheisha, son of Rav Idi, said: With regard to a stiff felt hat [sayna], it is permitted to wear it on Shabbat. The Talmud raises a difficulty: But wasn’t it taught in a baraita that wearing this hat is prohibited? The Talmud answers: It is not difficult. This baraita, which prohibits wearing a felt hat, is referring to a case where the hat extends a handbreadth from the person’s head and is therefore regarded as a tent; whereas that statement by Rav Sheisha, who permits doing so, is referring to a case where it does not extend a handbreadth from one’s head.

אלא מעתה: שרביב בגלימיה טפח, הכי נמי דאסור?

The Talmud is surprised at this answer: But if that is so, one who pulled his cloak a handbreadth beyond his head, is it also prohibited for him to do so? This is unreasonable, as it is an article of clothing, not a tent.

אלא, לא קשיא: הא ⁠— דמיהדק, הא ⁠— דלא מיהדק.

Rather, the previous explanation must be rejected, as the issue with regard to a felt hat is not whether it is considered a tent, but whether there is concern that one might come to carry it in the public domain if it falls from his head. This is not difficult; this statement of Rav Sheisha, which permits it, is referring to a case where the hat fits snugly on his head. There is no concern lest the hat fall and one will come to carry it; therefore it is permitted to wear it. Conversely, that baraita, which prohibits wearing this hat, is referring to a case where it does not fit snugly on his head. It is therefore liable to fall, and one might come to carry it in the public domain.