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# Subsets watch

1. Can the words bounded and closed be used synonymously when talking about subsets??
The same for open and unbounded.
2. No.
3. (Original post by DFranklin)
No.
Are they synonymous geometrically?? And if not may you please explain any difference. (I realise that I did not stipulate 'geometrically' before).

Thanks
4. is an unbounded closed subset of , and is a bounded open subset... so no.

Or if you want to think more geometrically, consider the plane . Then the x-axis is an unbounded closed set, and the open unit disc is a bounded open set.
5. (Original post by nuodai)
is an unbounded closed subset of , and is a bounded open subset... so no.

Or if you want to think more geometrically, consider the plane . Then the x-axis is an unbounded closed set, and the open unit disc is a bounded open set.
After this post, it is clear I have embarrassed myself with this question Cheers for the answers.
After this post, it is clear I have embarrassed myself with this question Cheers for the answers.
Not really, it takes a while to get used to coming up with really obvious sounding counter-examples.
7. Closed does imply bounded in a compact metric space. They're still not synonymous though.

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Updated: March 31, 2011
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