If $M$ is a Hausdorff $n$-manifold (without further assumption like paracompactness), given $x,y$ in $M$ is there a smooth function $f$ such that $f(x) \ne f(y)$?
Function seperating points
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differential-geometry
manifolds
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0Not assuming paracompactness seems odd; I've always seen it built into the definition of a smooth manifold. – 2012-03-05