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?
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?
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.