# Math Help - connected spaces

1. ## connected spaces

I know that the image of a connected space under a continuous map is connected, but what do you guys think about the pre-image of a connected space (still assuming a continuous map), is it necessarily connected?

2. Originally Posted by TXGirl
I know that the image of a connected space under a continuous map is connected, but what do you guys think about the pre-image of a connected space (still assuming a continuous map), is it necessarily connected?
No. Hint: think of konstant functions.

3. ## yes!!

Originally Posted by TXGirl
I know that the image of a connected space under a continuous map is connected, but what do you guys think about the pre-image of a connected space (still assuming a continuous map), is it necessarily connected?
Yes the pre-image has to be connected else the image would not be connected.