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\newtheoremstyle{theorem}{10pt}{0pt}{}{}{\bfseries}{\\}{10pt}{}\theoremstyle{theorem}\newtheorem{thm}{Theorem}[subsection]
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\begin{thm}\begin{enumerate}\item For any collection $\left\{G_\alpha\right\}$ of open sets, $\bigcup_\alpha G_\alpha$ is open.\item For any collection $\left\{F_\alpha\right\}$ of closed sets, $\bigcap_\alpha F_\alpha$ is closed.\item For any finite collection $G_1 , \ldots , G_n$ of open sets, $\bigcap_{i=1}^n G_i$ is open.\item For any finite collection $F_1 , \ldots , F_n$ of closed sets, $\bigcup_{i=1}^n F_i$ is closed.\end{enumerate}\end{thm}
Thanks,
Chris