$\left.\begin{array}{rr} (A\subseteq X)(B\subseteq Y)\Rightarrow \left(A\subseteq\overline{A}\right)\left(B\subseteq \overline{B}\right)\Rightarrow A\times B\subseteq \overline{A}\times \overline{B}\Rightarrow \overline{A\times B}\subseteq \overline{\overline{A}\times \overline{B}} \\ (A\subseteq X)(B\subseteq Y)\Rightarrow \left(\overline{A}\in C(X)\right)\left(\overline{B}\in C(Y)\right)\overset{?}{\Rightarrow} \overline{A}\times \overline{B}\in C(X\times Y)\Rightarrow \overline{\overline{A}\times \overline{B}}=\overline{A}\times \overline{B} \end{array}\right\}\Rightarrow $
$\Rightarrow \overline{A\times B}\subseteq \overline{A}\times \overline{B} \ldots (1) $
$--------------------------------------$
$\left.\begin{array}{rr} \left.\begin{array}{rr} \pi_1:X\times Y\to X \,\ (\tau_1\star\tau_2\mbox{ - }\tau_1) \text{ sürekli} \\ (A\subseteq X)(B\subseteq Y)\Rightarrow A\times B\subseteq X\times Y\end{array}\right\}\Rightarrow \pi_1\left[\overline{A\times B}\right]\subseteq \overline{\pi_1[A\times B]}=\overline{A} \\ \\ \left.\begin{array}{rr} \pi_2:X\times Y\to Y \,\ (\tau_1\star\tau_2\mbox{ - }\tau_2) \text{ sürekli} \\ (A\subseteq X)(B\subseteq Y)\Rightarrow A\times B\subseteq X\times Y\end{array}\right\}\Rightarrow \pi_2\left[\overline{A\times B}\right]\subseteq \overline{\pi_2[A\times B]}=\overline{B} \end{array}\right\}\Rightarrow $
$\Rightarrow \overline{A\times B} \overset{?}{\subseteq}\pi_1\left[\overline{A\times B}\right]\times \pi_2\left[\overline{A\times B} \right]\subseteq \overline{A} \times \overline{B} \ldots (2)$
$--------------------------------------$
$$(1),(2)\Rightarrow \overline{A\times B}=\overline{A}\times\overline{B}.$$
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