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## Main Question or Discussion Point

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?

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?