(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In topology, a f: X -> Y is continuous when

U is open in Y implies that f^{-1}(U) is open in X

Doesn't that mean that a continuous function must be surjective i.e. it must span all of Y since every point y in Y is in an open set and that open set must have a pre-image open in X, so there must be some x in X s.t. f(x) = y?

What is wrong with my logic?

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Continuous functions in topology

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