On the Theorems of Borsuk-Ulam and Ljusternik-Schnirelmann-Borsuk
1984 ◽
Vol 27
(2)
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pp. 192-204
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AbstractLet p ≥ 3 be a prime number and m a positive integer, and let S be the sphere S(m-1)(p-1)-1. Let f:S→S be a map without fixed points and with fp = idS. We show that there exists an h: S→ℝm with h(x) ≠ h(f(x)) for all x ∈ S. From this we conclude that there exists a closed cover U1,…, U4m of S with Uinf(Ui) = Ø for i = 1,…, 4m. We apply these results to Borsuk-Ulam and Ljusternik-Schnirelmann-Borsuk theorems in the framework of the sectional category and to a problem in asymptotic fixed point theory.
1976 ◽
Vol 66
(2)
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pp. 391-410
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2008 ◽
Vol 4
(2)
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pp. 203-245
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2015 ◽
Vol 17
(1)
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pp. 3-21
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1972 ◽
pp. 177-184
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1965 ◽
Vol 53
(6)
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pp. 1262-1264
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2002 ◽
Vol 30
(10)
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pp. 627-635
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