\documentclass{beamer}

\usepackage{graphics,epsfig, psfrag,color}
\newcommand{\darkblue}{rgb:red,1;green,2;blue,5}

\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{procedure}[theorem]{Procedure}



\title{Topological Data Analysis} 

\author{Graham Ellis \\
NUI Galway}

\date{\empty }

\begin{document}
\titlepage

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\frame{
\centerline{\textcolor{\darkblue}{\bf Homotopy 0-types}}

\vfill
\centerline{\textcolor{\darkblue}{$\pi_0(X) =$ set of connected components of $X$}}

\vfill

captures the \textcolor{\darkblue}{homotopy $0$-type} of a topological space $X$\onslide<2->,

\vfill
 and is a homotopy invariant: $X\simeq Y \Rightarrow \pi_0(X) = \pi_0(Y)$.
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\end{document}
