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Is there any bijection between closed unit interval and $R$?

Mirunalini_UML
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    There are many of them, but none of them are continuous. What have you tried? – Crostul Jan 20 '16 at 11:18
  • A little off topic, but your offhand remark has a neat idea behind it. At first I would expect there to be continuous bijections which are not homeomorphisms (indeed, this can be done for non-compact closed sets). But because the closed unit interval is compact, any continuous image of it must also be compact and in particular cannot be $\mathbb R$. – pre-kidney Jan 20 '16 at 11:21

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Yes, because they both have the cardinality of the continuum.

pre-kidney
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