Exercise · ZW-CONTINUOUS-IMAGE-OF-CONNECTED-SPACE-005 · ★★☆ Intermediate
For all these topologies on \(Y=\{a,b,c\}\), except one, there is a continuous surjection from some connected space . Which is the exception?
Choose one option.
A indiscrete: \(\varnothing,Y\) B \(\varnothing,\{a\},Y\) C \(\varnothing,\{a\},\{a,b\},Y\) D \(\varnothing,\{a\},\{b,c\},Y\) Show answer D. \(\varnothing,\{a\},\{b,c\},Y\)← Back to the question
Explanation The topology with open sets \(\varnothing,\{a\},\{b,c\},Y\) writes \(Y\) as the union of the disjoint open sets \(\{a\}\) and \(\{b,c\}\): \(Y\) is not connected and cannot be a continuous image of a connected space .
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