The Dude abides.

Turning a sphere inside out

Three questions:

1. Can you turn a circle inside out?
2. Can you turn a sphere inside out?
3. If you were a betting man (or woman, as it may be), and you were told either (1) or (2) were true, would you bet that the other question answers true as well?

Here is a mind blowing Google Video on topology that answers the questions!