# Find some extraordinary subset of [0,1]

## Homework Statement

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.

## The Attempt at a Solution

I tried some sets, but failed.

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

micromass
Staff Emeritus
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.