I'm so confused and can someone actually give me an explanation or a sentence or two. I would actually like to know what is going on in my math class. Please help me out!
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They are not topologically equivalent. A pair of sweat pants, no zipper, has 3 holes, 1 for each leg and 1 for your waist, in total 3 holes. A shirt has 4 holes, 1 for your neck, 1 for each arm and one for your waist. Since each has a different number of holes they are not topologically equivalent. To determine if they are equivalent, imagine that each is made out of rubber that can be stretched as much as you want. But the catch is that you can not tear or add holes. Since the pants have 3 holes, you can not stretch it in such a way that it will have 4 holes like a shirt. Imagine it this way, if you tried to put on a pair of pants as a shirt, there will be nowhere for your head to come out, so they cant be the same.