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Chapter 1 Topological Space Summary on Homeomorphism
MATH300 - Geometry and Topology
22 Pages • Topic Notes • Year: Pre-2021
1.1. How Do We Know That The Earth Isn’t Flat? “The world is flat and the greatest hoax of history is the assertion that it’s round.” I remember hearing this many years ago when I was at university. The claim was made at a lunchtime lecture given by a representative of the Flat Earth Society. Everyone in my physics class went along to heckle this “nut”. But we were stunned by the fact that he appeared to know far more physics than we did and every objection that we raised was answered by the most convincing and authoritative of explanations. The belief that light travels in straight lines is the illusion, he said. Ships appear to disappear over the horizon because the light is bending. And the fact that nobody has ever reached the edge of the world is because the closer you come to it, the smaller you become and the more slowly you travel while maintaining the illusion of constant speed. We’d heard of the Theory of Relativity and the lecturer’s explanations seemed to be consistent with what very vague understanding we had of that theory.
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