Let X_1, X_2 , ..., X_n be compact subsets of X.
<br>
Then there are finite open covers u_i of X_i for i=1, 2, .., n.
<br>
Suppose that X is a union of X_1, ..., X_n.
<br>
Then U, which is a union of finite open covers u_i, is to be finite open cover of X because finite union of finite sets is to be finite set again.
<br>
Therefore X is compact 입니다.
<br>
<!-- -->
