What is Topology?
<p>Every time, I would give them a slightly different answer, but I was never really satisfied with any of explanations. If you’ve ever googled topology, you will have no doubt encountered the animation of a doughnut morphing into a coffee mug. Most explanations I gave involved something related to this animation; how in topology a doughnut and a coffee mug are the same or how a sphere and a cube are the same. But an answer like this doesn’t really tell anyone what topology is really about, what is involved in actually working with topology nor explain why it’s even a worthwhile pursuit.</p>
<p>If you take an undergraduate course in general topology, you might struggle with relating what you’re learning to the familiar doughnut coffee mug animation. The purpose of this essay is to establish the basic concept of general topology and show how this concept is related to this familiar animation and other geometrical ideas. Next, we will have a look at why it is actually useful and interesting to consider doughnuts and coffee mugs to be the same things.</p>
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