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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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Density of function spaces

Let $\Omega$ be a subset of either $\mathbb{R}^n$ ($n\geq 3$, if it matters) or of a compact manifold. In either case, we'll call the manifold $M$. Let $V_i\subset V_{i+1} \subset \Omega$ be an increa …