# Hausdorff, locally connected and locally compact space reference.

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.