Are there non compact metric that has the following property?

Question

By definition, a metric space is said to be compact if for every open cover, it has a finite sub cover.

So I was wondering if there a case where a metric has some open cover that has a finite sub cover but some open cover doesn't have a finite sub cover and hence not compact by definition?

Answer 1

For every Metric space $X$, $X$ itself is a single open cover Which is a finite collection