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张丽丽  杨忠强 《数学进展》2007,36(3):349-353
令(X,d)是紧的度量空间,用↓USC(X)和↓LIP(X)分别表示从X到I所有的上半连续映射和所有Lipschitz映射的下方图形的全体.本文证明如果X是一个无限的紧的度量空间,则(↓USC(X),↓LIP(X))≈(Q,B(Q)),其中B(Q)=Q\(-1,1)~ω是Hilbert立方体Q=[-1,1]~ω的伪边界.  相似文献
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It is known that a strictly piecewise monotone function with nonmonotonicity height ≥ 2 on a compact interval has no iterative roots of order greater than the number of forts. An open question is: Does it have iterative roots of order less than or equal to the number of forts? An answer was given recently in the case of "equal to". Since many theories of resultant and algebraic varieties can be applied to computation of polynomials, a special class of strictly piecewise monotone functions, in this paper we investigate the question in the case of "less than" for polynomials. For this purpose we extend the question from a compact interval to the whole real line and give a procedure of computation for real polynomial iterative roots. Applying the procedure together with the theory of discriminants, we find all real quartic polynomials of non-monotonicity height 2 which have quadratic polynomial iterative roots of order 2 and answer the question.  相似文献
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