= Solution
A <compact topological group> is a group $G$ equipped with a compact Hausdorff topology for which multiplication $G\times G\to G$ and inversion $G\to G$ are continuous.
The <special unitary group> is
$$
SU(n)=\{U\in M_n(\mathbb C):U^*U=I,\ \det U=1\}.
$$
It is closed in the finite-dimensional real vector space $M_n(\mathbb C)$ because the equations $U^*U=I$ and $\det U=1$ are closed conditions. It is bounded because every column of a unitary matrix has norm one. The <Heine-Borel theorem> therefore makes it compact. Matrix multiplication is continuous, and inversion is continuous because $U^{-1}=U^*$. Hence \b[$SU(n)$ is a compact topological group].
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