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Howard Stauffer
Department of Mathematics, The National University of Malaysia, Kuala Lumpur
Astronomy Chemistry Earth & Planetary Sciences Mathematics Physics

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The Multiplication Problem for Spheres Howard Stauffer
Journal of Mathematical and Fundamental Sciences Vol. 9 No. 3 (1975)
Publisher : Institute for Research and Community Services (LPPM) ITB

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Abstract

Abstract. The multiplication problem for spheres is to determine which spheres in Euclidean space Sn-1 -"º En permit a continuous multiplication. This paper presents the topological K-theory proof that it is only possible when n = 1, 2, 4, and 8. These cases correspond to S0 -"º E1, S1 -"º E2, S3 -"º E4, and S7 -"º E8 where the multiplications are given respectively by the real numbers, complex numbers, quaternions, and Cayley numbers.  Ringkasan. Masalah pendarapan bagi bola adalah masalah untuk menentukan bola-bola dalam Ruang Euclid Sn-1 -"º En  membenarkan suatu pendarapan yang kontinu. Tulisan ini menyampaikan bukti teori K topologi bahwa hanya dapat terjadi abila n = 1, 2, 4, dan 8. Kasus ini bersesuaian dengan S0 -"º E1, S1 -"º E2, S3 -"º E4, dan S7 -"º E8 di mana pendarapan-pendarapan diberikan oleh bilangan-bilangan riil, kompleks, kuaternion, dan bilangan Cayley.
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