“In mathematics, a manifold is a topological space that locally resembles Euclidean space* near each point” (“Manifold,” Wikipedia, retrieved 6/10/2020). In other words, if you zoom in close enough to any point on a manifold, you won’t be able to tell the difference between what you see and a Euclidean space*. For example, if you zoom in close enough to a circle, it will look almost exactly like a straight line (ibid). This also works for most of a figure 8, but if you focus on the middle of the figure 8, no amount of zooming in will ever make it look like a single straight line (ibid).
There exists something called “Manifolds with a boundary.” “A manifold with boundary is a manifold with an edge. For example, a sheet of paper is a 2-manifold with a 1-dimensional boundary. The boundary of an [n-dimensional ‘manifold with a boundary’] is an (n−1)-[dimensional] manifold… A ball (sphere plus interior) is a 3-manifold with boundary. Its boundary is a sphere, a 2-manifold (ibid, italics added).”
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*What is the Gist of “Euclidean Space”?
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Disclaimer:
I am not a professional in this field, nor do I claim to know all of the jargon that is typically used in this field. I am not summarizing my sources; I simply read from a variety of websites until I feel like I understand enough about a topic to move on to what I actually wanted to learn. By definition, none of these posts address every aspect of a topic. If I am inaccurate in what I say or you know a better, simpler way to explain a concept, I would be happy to hear from you :).
