We are in chapter 3, mishnah 6. In the previous mishnah we learned that a guarded courtyard - a courtyard that provides security or privacy - can obligate a person to separate tithes just as an actual house does. Our mishnah discusses additional structures within the courtyard and around it, and how they are to be treated.
The Law of Roofs:
The mishnah opens with the law of roofs. The house stands within the courtyard, and a person may pass through the courtyard in order to bring his produce up to the roof. Does the roof of the house also obligate the separation of tithes? On this the mishnah says: "Hagagos peturin" - a roof does not have the status of a house. "Af al pi shehen shel chatzer hachayeves" - even if the area surrounding it is a courtyard of the type that obligates the separation of tithes, someone standing on the roof is not in the courtyard, since the roof is a separate domain in its own right.
This applies when the area of the roof is four amos by four amos, so that it has the status of a domain in its own right. In such a case the roof is only a roof: it is neither a courtyard nor a house, and therefore the obligation of tithing does not apply to it. But if the roof was less than four amos by four amos, it does not have the status of a domain in its own right, and it is most likely subordinate to the house according to the Rema, or subordinate to the courtyard according to the Bartenura - and then the laws will apply to it in accordance with the status of the courtyard.
Additional Structures in the Courtyard and Its Surroundings:
Beis sha'ar (gatehouse): the house alongside the gate - a small compartment placed at the entrance to the courtyard, in which the watchman would sit as a sort of home of his own. According to the Bartenura this is the entryway of the courtyard, and not the house.
Achsadra (portico): a roofed structure with columns. Three walls enclose it, and in place of the fourth wall stands a row of columns. The area behind the columns is protected and set apart, and it is a place in its own right that provides shelter from the rain, but it is not closed off by walls on all four sides. There was such a portico in the Beis HaMikdash, and this form of construction was common in Roman architecture.
Mirpeses (balcony): a combination of a balcony and a narrow walkway - an outer passage attached to the wall of the building, which provides access to the doors on the upper floor of the property.
In all of these cases the Tanna Kamma rules: "Harei elu k'chatzer" - the gatehouse, the portico and the balcony are considered an extension of the courtyard and part of it. That is, if this is a courtyard of the type that obligates in tithing, because it provides the required security or privacy, then the gatehouse, the portico and the balcony obligate as well; and if it is not a courtyard of the obligating type, they too do not obligate. In the words of the mishnah: "Im chayav, chayav; v'im patur, patur".