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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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815 views

Hölder functions dense in space of bounded continuous functions (for non-compact manifolds)

Let $M$ be a non-compact manifold and denote by $C_b(M)$ the space of bounded continuous functions on $M$. Is it true that the space of Hölder functions is dense in $C_b(M)$ (in the $C^0$ norm: $||f|| …