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

Video | Posted on by | Tagged , , , , , , , , , , , , , | Leave a comment

Pictures of the 3-sphere, or should I say the 4-ball? It’s a 4-dimensional 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

Image | Posted on by | Tagged , , , , , , , , , | Leave a comment

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 Borsuk-Ulam Theorem. (one of its corollaries is that subsets of Rⁿ are not homeomorphic to Sⁿ)   CONFORMAL Gerardus Mercator’s projection preserves angles … Continue reading

Posted in Uncategorized | Tagged , , , , , , , , , | Leave a comment