Solution (source code)

= Solution

A <topological space> is <compact> if every <open cover> has a <finite subcover>:
$$
\boxed{X=\bigcup_{i\in I}U_i,\ U_i\text{ open}\ \Longrightarrow\ X=U_{i_1}\cup\cdots\cup U_{i_n}\text{ for finitely many indices}.}
$$
There is no <Hausdorff> requirement in this definition.