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1. The quotient space R2/∼ is homeomorphic to the torus. Parallel lines in R2 are identified, resulting in a torus shape. 2. For a space X and subset A, the quotient space X/A identifies all points in A to a single point. This collapses A to a point. 3. The torus T2 can be constructed as a quotient space of the square [0,1]x[0,1] with opposite edges identified. A map is given that shows the torus is homeomorphic to the surface of a doughnut in R3.

Author

ducquang00

Language

EN