smooth manifold

This paper makes an extension of the map from a sphere into an euclidean space to the mapof a sphere into a smooth manifold by means of the cyclic transformation theory of algebraic topology, gaining Borsuk-Ulam type of theorem.

应用代数拓扑学中周期变换的理论，将球面到欧氏空间的映射推广到从球面到光滑流形映射的情形，从而得到了Brosuk－Ulam型定理。

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