Suppose that $(X,d)$ and $(Y,d)$ are metric spaces between which there exists a continuous function. Fix $x \in X$ and $y\in Y$. When does there exist a continuous function sending $x$ to $y$?
2026-04-07 23:14:53.1775603693
Existence of Continuous Function respecting points
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Define $f(z):=y$ for all $z \in X.$ Then $f$ is continuous anf $f(x)=y.$