Editing Box topology (section)

=== Example — failure of compactness ===
Consider the countable product <math>X = \prod_{i \in \N} X_i</math> where for each ''i'', <math>X_i = \{0,1\}</math> with the discrete topology. The box topology on <math>X</math> will also be the discrete topology. Since discrete spaces are compact if and only if they are finite, we immediately see that <math>X</math> is not compact, even though its component spaces are. 

<math>X</math> is not sequentially compact either: consider the sequence <math>\{x_n\}_{n=1}^\infty</math> given by 
:<math>(x_n)_m=\begin{cases}
  0 & m < n \\
  1 & m \ge n 
\end{cases}</math>
Since no two points in the sequence are the same, the sequence has no limit point, and therefore <math>X</math> is not sequentially compact.