Given a finite open cover ${\mathcal A}=\{A_1,A_2,\cdots,A_n\}$ of a Hausdorff space, what is the general form of the compact space?
Can it be of the following form: \begin{eqnarray} K=K_1\cup K_2\cup\cdots K_n \end{eqnarray} where $K_i\subset A_i$ is compact.
Can the condition be relaxed, e.g. infinite open cover, or any other condition to be imposed so that we can get any other argument?