I am reading the book of Munkres Topology and it says for a given "normal space" with finite open covering, the set complement of X with union of open coverings without a covering, it's closed. The formal notation is following:
Thus at the above given, can't understand how A is concluded as a colsed so fast. It looks it's dervied from the fact of it is normal space, but can't make it connected how the concept of normal - which is sepratibility of two sets of each one's neigborhood- could derive the fact that A is closed.
Any hint?
The set $A$ is the complement of the union of $U_2$ through $U_n$. Since $U_2,\ldots,U_n$ are open, their union is also open, and hence the complement of that union is closed. This is just very basic topology so far—no reference to normality is needed at this point.