Some Partitions Consisting of Jordan Curves
نویسنده
چکیده
Some decompositions of the three-dimensional sphere and three-dimensional ball into Jordan curves are considered. In particular, it is proved that for every strictly positive real number p ≤ 1 there exists a partition of the unit three-dimensional Euclidean sphere into circles whose radii are equal to p. Let S2 be the unit two-dimensional sphere in the Euclidean space R3 and let S3 be the unit three-dimensional sphere in the Euclidean space R4. The well-known Hopf fibration φ : S3 → S2 can be expressed analytically as φ(x1, x2, x3, x4) = (z1, z2, z3),
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