# complex question

• March 25th 2011, 05:08 PM
shaheen7
complex question
similarly there is another question i am stuck on.

Give an example of a subset E of the complex plane which is connected, neither open nor closed, has nonempty interior, and is unbounded.

I sort of figured out at least for the neither open/closed and unbounded part that perhaps getting the union of a compact set and a non-intersecting open, un-bounded set.

Any suggestions?
• March 25th 2011, 05:38 PM
tonio
Quote:

Originally Posted by shaheen7
similarly there is another question i am stuck on.

Give an example of a subset E of the complex plane which is connected, neither open nor closed, has nonempty interior, and is unbounded.

I sort of figured out at least for the neither open/closed and unbounded part that perhaps getting the union of a compact set and a non-intersecting open, un-bounded set.

Any suggestions?

$\displaystyle{\{\,z\in\mathbb{C}\,\,;\,\,Re(z)\geq 0\,,\,\,0\leq Im(z)<\pi\,\}$

Tonio