amsthm.tex

\documentclass{article}

\usepackage{amsthm}

\newtheorem{defn}{Definition}
\newtheorem{claim}{Claim}

 
\begin{document}

\begin{defn}
A \textbf{topology} $\mathcal{T}$ on a set $X$, denoted $\mathcal{T}(X)$, is a subset of $2^X$ (the powerset of $X$) satisfying...
\end{defn}

\begin{claim}
Suppose $X$ is a set and $\mathcal{T}$ is a topology on $X$. Then $\mathcal{T}$ is great.
\end{claim}

\begin{proof}
Left as an exercise for the reader.
\end{proof}

\end{document}