Rambam - 1 Chapter a Day

At the same time. If, however, he is no longer standing over or holding the corpse, he does not impart impurity to keilim by standing over them [the Rambam’s Commentary to the Mishnah (Ohalot 15:9)].

Obviously, in most cases, a handbreadth is the width of a grown person’s hands. The Rambam (ibid.) explains that this clause refers to a child or a youth with very small hands.

And he and they are pure.

I.e., his inner cavity is not one solid mass.

And thus can be considered as an ohel.

Chapter 12, Halachah 1; Chapter 13, Halachah 4.

If the door to the house was open at the time the corpse passed under the roof of the exedra, the impurity would spread from the exedra to the house (see Chapter 7, Halachah 3). In his Commentary to the Mishnah (Ohalot 6:2), the Rambam explains that we are speaking about a situation where the door was closed and the person attempted to lock it to prevent it from being opened and causing the house to become impure.

Without a person holding it closed. According to the Rambam (op. cit.), even if the key is what keeps it closed, the house does not become impure. Others maintain that the door must be able to remain closed even without a key.

By holding the door shut.

Our translation is taken from the Rambam’s Commentary to the Mishnah (op. cit.). There he explains that the oven was entirely inside the house, but the dome-shaped building was outside the house.

In his Commentary to the Mishnah (Ohalot 5:1), the Rambam describes this opening as being on the curve of the oven, close to the ground, through which fire is inserted and ashes are taken out.

The bracketed additions are made on the basis of the Rambam’s Commentary to the Mishnah (op. cit.).

Since the oven is resting on or built into the ground, it is considered as a separate entity and not as a k’li contained within the house. See Kessef Mishneh. The Ra’avad offers a different explanation.

I.e., one capable of holding more than 40 se’ah in which instance, it can never contract ritual impurity. See Chapter 6, Halachah 2.

Because as stated in Chapter 13, Halachah 3, such a vessel intervenes in the face of ritual impurity.

This is speaking about an instance where there is no other entrance through which the impurity can depart and the closet is blocking the doorway entirely. Since the impurity seeks to depart, it pierces through the closet and enters its inner space (Kessef Mishneh).
It must be emphasized that Chullin 125b and many commentaries to the Mishnah follow a different version and rule that the closet is pure.

Our translation is taken from Rav Kappach’s translation of the Rambam’s Commentary to the Mishnah (Keilim 18:2). Others offer different interpretations. Diagram

Although Ohalot 4:3 mentions three fingerbreadths, the Rambam understands this as meaning anything less than a handbreadth.

Were it to be able to be separated from the closet, it would be considered as an independent k’li. Hence, it could contract impurity and spread impurity throughout the house.

Including not only the portion that extends from behind the closet, but also the space it comprises within the closet.

Because the impurity pierces through and ascends and thus enters the inner space of the house.

Provided the doors to the closet are closed.

Thus if the impurity is in the closet, the house is impure, because the impurity will ultimately depart even though the opening to the chest is less than a handbreadth.

And thus those keilim are considered as if they were inside the closet.

For the impurity is within the house. Even if it is considered as being under a separate covering, when there is one ohel under a second ohel, everything under the second ohel is impure [Rambam’s Commentary to the Mishnah (Ohalot 4:1)].

Our translation is based on the Rambam’s Commentary to the Mishnah (op. cit. 4:1).

In the above source, the Rambam explains that the closet was of hollow walls with boards on either side. The Mishnah — and this halachah — is speaking about an instance when there was either impurity or keilim between those boards.

I.e., anything less than a hand breadth. Diagram

It does not matter if the impurity is under a portion that is within a handbreadth of the ground or under a portion that is above a handbreadth. As long as part of the slanted wall is a handbreadth above the ground, it is considered as part of an ohel and conveys impurity to everything in the structure. There must, however, be a straight roof of at least a handbreadth by a handbreadth (see Chapter 12, Halachah 1; Hilchot Sukkah 5:25).

We are speaking about a wall that is made out of fabric, e.g., linen or wool, or leather (Chapter 5, Halachah 12). Therefore, even though it is considered as part of an ohel, it still contracts ritual impurity like a k'li.

The Kessef Mishneh states that this refers to an instance where the corpse was removed before the person touched the wall of the tent. Otherwise, he would contract the impurity that lasts seven days.

The impurity is combined and considered as an entire olive-sized portion despite the fact that half is inside the tent and half is outside. Nevertheless, since it is divided, it only conveys impurity that lasts until the evening rather than impurity that lasts for an entire week (Kessef Mishneh).

And only the articles directly above or directly below the impurity contract impurity. The structure as a whole is not considered as impure. The part that is spread out on the ground is not considered as an extension of the walls of the tent, but rather a covering over the ground.