Abstract: Hurewicz-Radon theorem [1] gives a sufficient and necessary condition about the existence of an orthogonal multiplication f:R^k×Rⁿ→Rⁿ. In this paper,we shall discuss two extensions of the theorem.that is,the sufficient and necessary conditions about the existence of an orthogonal multiplication f:R^k×Rⁿ→Rⁿ⁺¹ or f:R^k×Rⁿ→Rⁿ⁺²

Key words:  , orthogonal multiplication, Hurewicz-Radon theorem, topological K-theory ,