\documentclass{article}
\thispagestyle{empty}
%\def\pgfsysdriver{pgfsys-tex4ht.def}
\usepackage{tikz}
\newcommand{\R}{R}
\tikzstyle{sikorski} = [blue]
\tikzstyle{frolicher} = [green]
\begin{document}
\begin{tikzpicture}
\draw (0,0) grid (6,4);
\draw[ultra thick] (0,1) -- (6,1);
\draw[ultra thick] (3,0) -- (3,4);
\draw[ultra thick,sikorski] (0,0.9) -- node[pos=.5, auto=right,black] {\(X\)} (3,0.9) parabola  (6,4) node[black] at (4.5,2.7) {\((t,t^2)\)};
\draw[ultra thick, frolicher] (0,1.1) -- node[pos=.5, auto=left,black] {\(Y\)} (2.9,1.1) -- (2.9,4);
\node at (3,4.5) {\(X, Y \subseteq \R^2\) as};
\end{tikzpicture}
\end{document}