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Constructing the Torus - Topology #2

14.2K views
Nov 8, 2019
20:13

Notes are on my GitHub! github.com/rorg314/WHYBmaths In this video I start by giving a way to represent the pairs of a cartesian product as a rectangular region. We then use this concept to take the cartesian product of two circles to construct the torus, T^2 = S^1 x S^1. We see that this produces a rectangle with opposite edges identified. I demonstrate how this then produces the homeomorphism between this region (fundamental polygon) and the torus.

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Constructing the Torus - Topology #2 | NatokHD