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PostPosted: Wed Nov 11, 2015 4:18 pm 

Joined: Mon Nov 09, 2015 11:52 am
Posts: 75
Location: Limassol/Pyla Cyprus
This is a question I posted in the old forum but remained unanswered. Let us see if it will have a better fate this time.

Decide whether you can find uncountably many disjoint subsets of \(\mathbb{R}\) such that each of them is order-similar to \(\mathbb{R}.\) (I.e. for each of them there is a bijection with \(\mathbb{R}\) which preserves the ordering.)


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