Descriptive complexity of function spaces

In this paper we show that $ {C_\pi }(X)$ topologized by the pointwise convergence topology, can have arbitrarily high Borel or projective complexity in $ {{\mathbf{R}}^X}$ is a countable regular space with a unique limit point. In addition we show how to construct countable regular spaces $ X$ $ {C_\pi }(X)$ <IMG WIDTH="38" HEIGHT="22" ALIGN="BOTTOM" BORDER="0" SRC="images/img11.gif" ALT="$ {{\mathbf{R}}^X}$">.