This is not a homework problem, just something I was thinking about. In a general metric space, is it true that every closed set can be expressed as the intersection of an infinite collection of open sets? I don't really know where to begin. Since the finite intersection of open sets is open, and the infinite intersection of open sets may or may not be open or closed, this suggests to me that the statement may not be true; however, I'm not sure how I would use this fact to construct a counter-example. Any help is much appreciated!