I am trying to understand the definition of compact sets (as given by Rudin) and am having a hard time with one issue. If a finite collection of open sets "covers" a set, then the set is said to be compact. The set of all reals is not compact. But we have for example: C1 = (-∞, 0) C2 = (0, +∞) C3 = (-1, 1) ℝ ⊆ C1 ∪ C2 ∪ C3 The first thing I can think of as a problem is that the endpoints of two of the sets are infinities. But when I read the definition of an open set, that doesn't seem to pose a problem. What am I missing?