The first number of perakim of masechet Keilim deal with the laws of tumah as they related to klei cheres (earthenware utensils). What is unique about klei cheres is that they only attract tumah if the source of tumah is inside the kli (vessel); even if it is only in its airspace. The Mishnah (2:7) discusses the case of a tray, with multiple bowls connected to its surface.
The Mishnah teaches that iff one of the bowls become tameh, the others remain tahor. If however the rim around the edge of the tray is taller than the height of the bowls, then if one of the bowls become tameh so do the others. The Bartenura explains that in the latter case, since the rim is higher than the bowls, even before the source of tumah reached one of the bowls, it was within the airspace of the tray. That being the case the entire tray became tameh along with the bowls connected to it.
The Tosfot R' Akiva Eiger however finds this explanation difficult, considering that the Mishnah rules that a wooden spice box, with multiple compartments, would also share the same law. Note that for a wooden utensil to become tameh the source of tumah must be in direct contact with the kli. In other words, the explanation of the Bartenura would not work for the spice box. The Tosfot R' Akiva Eiger instead cites the explanation of the Rash that when the rim of the tray is higher than the bowls, it is all considered one kli. When it is lower, the bowls are considered independent keilim. R' Akiva Eiger notes however that the Rambam explains like the Bartenura in our case, yet explains like the Rash in the case of the scribe's box that has multiple compartments.
The Rav (Igrot HaGrid HaLevi, Keilim 5:6-7) however notes that the Rambam explains that this tray that has the bowls connected to it, is considered one kli. The Rambam's statement does not appear to differentiate regarding the height of the rim and simply rules that it is one kli. That being the case, the height of the rim around the tray does not affect whether it and the bowls are considered one kli. That being the case, what difference does the height of the rim make?
The Rav explains that this Mishnah teaches us a unique law regarding klei cheres with respect to tumat avir (attracting tumah by way of tumah being in the airspace). Unlike other keilim for klei cheres, tumat avir is not dependant on whether the various components are considered one kli. What is important for a kli cheres is whether there is one "inside" or not. If there are many distinct insides, then they are treated separately.
The Rav uses this explanation to explain the debate regarding whether a partition can divide an earthenware oven. R' Eliezer maintains it can, while the Chachamim disagree. The Rav asserts that R' Eliezer agrees that a partition does not turn one kli into two. R' Eliezer however argues that the partition does however change the oven, in that it has two insides. That being the case, if tumah is inside one side, food that is on the other side of the partition remains tahor. The Chachamim do not disagree with this principle. They instead maintain that the introduction of a partition does not create two insides.1
Returning to our Mishnah we can suggest that when the Bartenura explains that the tumah reaches the airspace of the tray prior to reaching the cups, it is not just to explain that the tray becomes tameh first, but illustrating that the taller rim makes the tray considered as if it has one inside.2
1 See inside where this Mishnah and the case of the gistra are discussed at length.
2 One may suggest that the reason why the Rambam explains our case and the kalmarin and beit hatavlin differently is because the reason why the rim impacts these keilim is different. For klei cheres, what is important is determining the insides. For the beit hatavlin, considering it is made of wood, what is important is whether it is defined as a single kli. The case of the kalmarin requires further thought.
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