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What exactly is topology ??

So I was reading this, about the practical application of topology.

I wanted to ask what exactly is in it---as a subject what is studied in this field.

I have seen videos wherein they oversimplify tell us that in topology, you squeeze and stretch but don't cut, or how a donut and a mug is equivalent. (I think it must be like simplifying calculus and saying that it's just fancy addition.)

How does it help in mathematics, because it is studied as a full fledged course, it must have its perks and used too.... [ Also considering that there are so many tags under this topic on SE ] ??

(I am still in high school so I don't have a lot of information, but I consider myself to be a curious math enthusiast)



from Hot Weekly Questions - Mathematics Stack Exchange

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