Question:
True/False?
There exists a continuous surjective map from the complex plane onto the non-zero reals.
Hint:
Search for topological invariants.
Discussion:
Under a continuous function, connected set must go to connected set. The complex plane (\mathbb{C}) is connected.
It's image must be connected.
(\mathbb{R}-0) is not connected.
So the statement is False.
