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Tag Archives: homeomorphism
Why bicontinuity is the right condition for topological equivalence (homeomorphism): if continuity of the inverse isn’t required, then a circle could be equivalent to a line (.99999 and 0 would be neighbours) — Minute 8 or so. Geometric construction (no … Continue reading
Pictures of the 3sphere, or should I say the 4ball? It’s a 4dimensional circle. Even though these drawings of it look completely sweet, I have a hard time parsing them logically. They’re stereographic projections of the hypersphere. All they’re trying … Continue reading
Maps, projections, and hairy balls
Fact: a map of the Earth can either accurately depict areas, or accurately depict angles. But not both. Thanks for the info, The BorsukUlam Theorem. (one of its corollaries is that subsets of Rⁿ are not homeomorphic to Sⁿ) CONFORMAL Gerardus Mercator’s projection preserves angles … Continue reading
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Tagged BorsakUlam theorem, education, homeomorphism, maps, math, mathematics, maths, R^n, science, S^n
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