Hi,

Can one please help me with the following game:

Attachment 20060

I just can not find a set.

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- Dec 11th 2010, 03:37 AM1234567metric space sets
Hi,

Can one please help me with the following game:

Attachment 20060

I just can not find a set. - Dec 11th 2010, 03:54 AMFernandoRevilla
A little help:

**(i)**$\displaystyle A$ closed, bounded and compact is possible.

Choose $\displaystyle A=\{0\}$

**(ii)**$\displaystyle A$ closed, not bounded and compact is impossible because:

$\displaystyle A$ is compact iff $\displaystyle A$ is closed and bounded.

...

Fernando Revilla - Dec 11th 2010, 03:56 AMPlato
With sixty other postings, you should understand that this is not a homework service nor is it a tutorial service. So you need to show some of your own work on this problem or explain what you do not understand about the question.

Here is a start. $\displaystyle [0,1]$ is closed, bounded, and compact.

$\displaystyle (0,\infty)$ is not closed, not bounded, and not compact. - Dec 11th 2010, 04:01 AM1234567

Hi sorry about this.

I have considered some cases:

1 A union of closed and bounded set atr compact.

i.e [0,1] U [2,3]

2. (0,1) not closed so not compact

3. {1/n, n=1,2,3,...} U {0} compact bounded and closed

4. empty set compact bounded and closed

5. set**R of all real numbers.**Not compact - Dec 11th 2010, 05:04 AM1234567
I don't understand what the question asks about the different possibilites

- Dec 11th 2010, 05:27 AMPlato
Think of a truth-table

$\displaystyle \begin{array}{*{20}c} {closed} &\vline & {bounded} &\vline & {compact} \\\hline

Y &\vline & Y &\vline & Y \\

Y &\vline & Y &\vline & N \\

Y &\vline & N &\vline & Y \\

Y &\vline & N &\vline & N \\

N &\vline & Y &\vline & Y \\

N &\vline & Y &\vline & N \\

N &\vline & N &\vline & Y \\

N &\vline & N &\vline & N \\ \end{array} $

I gave you the answers for the first line and the last line. - Dec 11th 2010, 07:18 AM1234567