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Is there a Hausdorff topological space $X$ such that for any continuous map $f: X\longrightarrow \mathbb{R}$ and any $x\in X$$x\in \mathbb{R}$, the set $f^{-1}(x)$ is either empty or infinite?
Is there a Hausdorff topological space $X$ such that for any continuous map $f: X\longrightarrow \mathbb{R}$ and any $x\in X$, the set $f^{-1}(x)$ is either empty or infinite?
Is there a Hausdorff topological space $X$ such that for any continuous map $f: X\longrightarrow \mathbb{R}$ and any $x\in \mathbb{R}$, the set $f^{-1}(x)$ is either empty or infinite?
Is there a Hausdorff topological space $X$ such that for any continuous map $f: X\longrightarrow \mathbb{R}$ and any $x\in X$, the set $f^{-1}(x)$ is either empty or infinite?
