# Homework Help: Find some extraordinary subset of [0,1]

1. Nov 17, 2011

### Maclaurin

1. The problem statement, all variables and given/known data
I want to find a subset A of [0,1] such that A=cl(int A) and bd A does not have measure zero where cl means closure and int means interior.

2. Relevant equations

3. The attempt at a solution

I tried some sets, but failed.

2. Nov 17, 2011

### micromass

3. Nov 17, 2011

### Maclaurin

I tried that set but it was difficult for me to modify it. Can you give me more hint?

4. Nov 17, 2011

### micromass

Well, you want the fat Cantor set to be the boundary of the set you want.

Every step you leave out some open intervals. Now let V be the union of the open intervals you leave out at the odd steps. Take $\overline{V}$ to be your set.

5. Nov 18, 2011

### Maclaurin

I think bd of V is not the fat Cantor set..... what should I do?

6. Nov 18, 2011

### Maclaurin

ah instead of bd of V, boundary of closure of V.