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A new and constructive proof of the Borsuk-Ulam theorem. (English) Zbl 0397.55004


MSC:

55N20 Generalized (extraordinary) homology and cohomology theories in algebraic topology
57N10 Topology of general \(3\)-manifolds (MSC2010)
57N15 Topology of the Euclidean \(n\)-space, \(n\)-manifolds (\(4 \leq n \leq \infty\)) (MSC2010)
57Q99 PL-topology
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References:

[1] Karol Borsuk, Drei Sätze über die n-dimensional euklidische Sphäre, Fund. Math. 20 (1933), 177-190. · Zbl 0006.42403
[2] B. Curtis Eaves, A short course in solving equations with PL homotopies, Nonlinear programming (Proc. SIAM-AMS Sympos., NewYork, 1975) Amer. Math. Soc., Providence, R. I., 1976, pp. 73 – 143. SIAM-AMS Proc., Vol. IX.
[3] B. Curtis Eaves and Herbert Scarf, The solution of systems of piecewise linear equations, Math. Oper. Res. 1 (1976), no. 1, 1 – 27. · Zbl 0458.65056 · doi:10.1287/moor.1.1.1
[4] Erika Pannwitz, Eine freie Abbildung der \?-dimensionalen Sphäre in die Ebene, Math. Nachr. 7 (1952), 183 – 185 (German). · Zbl 0049.40304 · doi:10.1002/mana.19520070306
[5] Colin Patrick Rourke and Brian Joseph Sanderson, Introduction to piecewise-linear topology, Springer Study Edition, Springer-Verlag, Berlin-New York, 1982. Reprint.
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