Exercise · ZW-CONTINUOUS-IMAGE-OF-CONNECTED-SPACE-004 · ★★☆ Intermediate
Let \(X=\{1,2,3\}\) with open sets \(\varnothing,\{1\},\{1,2\},X\) and \(Y=\{a,b\}\) with open sets \(\varnothing,\{a\},Y\). How many continuous maps \(f:X\to Y\) are surjective?
Choose one option.
A 1 B 3 C 4 D 2 Show answer ← Back to the question
Explanation Surjective requires \(f^{-1}(\{a\})\) to be open, nonempty and different from \(X\): only \(\{1\}\) or \(\{1,2\}\). There are 2.
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