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Answer by Yousuf Soliman for Does metrizable, locally compact and...
$\newcommand{\veps}{\varepsilon}$For every $x\in M$ let $\veps_x>0$ be such that $B(x,\veps_x)$ admits a compact closure. Since the following family is an open cover of $M$:...
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Let $M$ be a locally compact and metrizable space. If $M$ is $\sigma$-compact, prove $C_{0}(M)$ is separable.In addition, discuss whether or not there is a natural way to weaken the hypotheses. For...
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