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If you stick a cork in the bottom, his bottles have an inside and an outside.

The abstract object doesn't, the 3d manifestation of it does.

I had to think about what that meant for a moment, as it's sort of part of the weirdness of the bottle. Really, putting a cork in it is probably closer to putting a lid on a bowl, no?

It's just sealing the local minimum. (Maximum? I don't really know what the sign should be for this. Probably maximum, for enclosed volume, since I'm not sure if it's reasonable to talk about the topology having a minimum in this context...)

If I needed to close one, I'd stick a cork in the hole in the bottom. So I think that is a reasonable way to describe closing it.

I don't think I can reason clearly about the 4 dimensional object, part of pointing out that a 3d manifestation does not have the same properties is me trying to do that.

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