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\title On the Rational Homotopy Type of Function Spaces\endtitle
\author Edgar H. Brown, Jr. and Robert H. Szczarba\endauthor
\abstract The main result of this paper is the construction of a
minimal model for the function space $\Cal F(X,Y)$ of continuous
functions from a finite type, finite dimensional space $X$ to a
finite type, nilpotent space $Y$ in terms of minimal models for $X$
and $Y$. For the component containing the constant map,
$\pi_*(\Cal F(X,Y))\otimes Q =\pi_*(Y)\otimes H^{-*}(X;Q)$
in positive dimensions. When $X$ is formal, there is a simple
formula for the differential of the minimal model in terms of the
differential of the minimal model for $Y$ and the coproduct of
$H_*(X;Q)$. We also give a version of the main result for the space
of cross sections of a fibration. \endabstract
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