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Let [tex]f: X \to Y[/tex] a continu surjection (onto).

1. If [tex]X[/tex] is connected then [tex]Y[/tex] connected?

2. Suppose [tex]Y[/tex] is connected. When is [tex]X[/tex] connected?

1. This is true, because [tex]f[/tex] is continu

2. I'm wondering, do I have to add a condition to the function [tex]f[/tex] or do I have to give a topology on [tex]Y[/tex] wherefore [tex]X[/tex] is connected? If yes, how?

Thanks in advance!

1. If [tex]X[/tex] is connected then [tex]Y[/tex] connected?

2. Suppose [tex]Y[/tex] is connected. When is [tex]X[/tex] connected?

1. This is true, because [tex]f[/tex] is continu

2. I'm wondering, do I have to add a condition to the function [tex]f[/tex] or do I have to give a topology on [tex]Y[/tex] wherefore [tex]X[/tex] is connected? If yes, how?

Thanks in advance!

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