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This is the problem: I have a space $X=\{a,b\}$ with trivial topology (open sets are empty set and whole $X$) and continuous map $f\colon X\to Y$. ($Y$ is arbitrary space). Can I conclude that $f(a)=f(b)$ because original of some open set in $Y$ is $\{a,b\}$, and original of some closed set in $Y$ is $\{a,b\}$? My friend used it but I don't agree.

3 Answers 3