[dec0dedab0de]

Maybe I'm being thick, but they clearly have an inside. Your link does not mention anything about not having an inside.

[dazmax]

It's a joke. It has an inside as much as any bottle does, but the only point of a Klein Bottle is the topological form so they're using topological language to talk about it.

[dec0dedab0de]

If you see my reply to the sibling I figured it out. However, thanks for confirming.

[DanBC]

Does a möbius strip have an inside or outside? The klein bottle is similar. The inside is the outside.

[dec0dedab0de]

I think maybe it's just semantics. I seem to be incorrectly assuming that the inside of the bottle is the space where the liquid goes. And the inside of the möbius strip would be the gap where you put your neck if you were to wear it as a necklace.

Would it be more correct to say that there is no inside surface? And it was just a pun that went over my head?