SOME HOMOTOPY PROPERTIES OF n-FOLD SYMMETRIC PRODUCT OF THE SPACE X

In this paper, we study some homotopy properties of the space n-fold symmetric product of thespace X. We prove that if mappings f; g : X ! Y are homotopic, then the mappings Fnf;Fng :FnX ! FnY are also homotopic. Also shown that the functor of n-fold symmetric product Fn is acovariant homotopy functor. Besides proved that if spaces X and Y are homotopically equivalent,then the spaces FnX and FnY are also homotopically equivalent.

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