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I know a set like $(a, b)$ with $a < b$ is an interval on the reals (in particular, this one happens to be an open interval on the usual topology on $\mathbb{R}$, but I'm not specifically interested in open intervals here). Consider a set like $S = (a, b)\cup (c, d)$ where $-\infty < a < b < c < d < \infty$. Is there any standard term for sets like S that are comprised of the union of a finite number (probably 2) of disjoint intervals (where each such interval might open, closed, or neither)?

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«Union of disjoint intervals» is a pretty standard term. I doubt there is better. – Mariano Suárez-Alvarez♦ Sep 7 '12 at 22:11
Although not an interval, $S$ is open because it is the union of open sets. – Fly by Night Sep 7 '12 at 22:25
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And every open subset of the reals is a union of (possibly infinitely many) disjoint open intervals, so in a sense the term you are looking for is "open set". If you allow unions of closed intervals, it's even simpler - the term you are looking for is "set". – Gerry Myerson Sep 7 '12 at 23:00
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@MichaelMcGowan: It's okay if Gerry's suggestion is not what you're looking for, but could you try to say so without sounding like you're berating him and Fly by Night for trying to help you? When you use fuzzy terminology such as "like" in your question, you're implicitly inviting the reader to guess which generalization of your example you're thinking of. That's alright, especially when the real question is something like "how should I generalize this" -- but please don't tell people off for guessing wrong. – Henning Makholm Sep 8 '12 at 1:26
Michael, I was trying to tell you, and any other readers, something you/they might not know and might find interesting, whether it relates to your unstated restrictions or not. I'm sorry if I have taught you something you did not want to learn. – Gerry Myerson Sep 8 '12 at 3:20
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