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I would like to find a reference to the following proposition:

Let $X$ a Hausdorff, locally compact, locally connected, connected space and $K \subseteq X$ a compact subset. Then, there exists a compact and connected subset M such that $K \subseteq M$.

The proof is just an easy application of the chain definition of connectedness and I have no problem with it. I just need a reference to that.

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