(a) Suppose that $f:\mathbf{R}\to\mathbf{R}$ is ``continuous from the right'', that is, $\displaystyle{ \lim_{x\to a+}f(x)=f(a),}$ for each $a\in\mathbf{R}$ . Show that $f$ is continuous when considered as a function from $\mathbf{R}_{\ell}$ to $\mathbf{R}$ . (b) Can you conjecture what functions $f:\mathbf{R}\to\mathbf{R}$ are continuous when considered as maps from $\mathbf{R}$ to $\mathbf{R}_{\ell}$ ? As maps from $\mathbf{R}_{\ell}$ to $\mathbf{R}_{\ell}$ ?
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