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I'm pretty sure it's possible to find a biijection from (a,b) to [c,d], but as far as proving them not homeomorphic, is it sufficient to say that the endpoints can't map to each other since the open interval does not contain its LUB and GLB? My other thought was proving the bijjection between them can't be continuous.

The question does not say whether these are in the real line or any other particular space.

Peace Blaster
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    Think about what happens if you were to remove one of the end points of $[c,d]$. – user332239 Nov 26 '16 at 21:03
  • For $(a, b)$, removing any point yields a set with two connected components. Alternatively, $[c, d]$ is compact. – AJY Nov 26 '16 at 21:04
  • You have to assume that they’re in the real line: they’re clearly in some linearly ordered space, and there are spaces in which they could be homeomorphic. You can use @user332239’s suggestion, or you can think about compactness. – Brian M. Scott Nov 26 '16 at 21:05

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