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It's asserted that a topologist can't tell a coffee mug from your doughnut (you'll be able to deform one in the other) which is the attitude you must take towards questions for this kind.
Out of this perspective, a rip is the identical thing because bottom on the kit is the same like a sleeve: it is possible to deform each of them in the other, so topologically they're the same.
(Imagine making the rip bigger, or squashing long sleeve right short sleeve.
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) They are all just instances of what topologists call punctures.
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I not really know the solution to your current question, but one property a surface have to have as a way to be turned internally is that it should be orientable.
basically, it should experience an inside plus an outside in the first place.
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