Does there exists any locally compact haussdoff space $(X, \tau) $ which is totally disconnected but not zero dimensional?

Question

• $(X, \tau)$ is zero dimensional if it has a clopen basis.

• $(X, \tau)$ is totally disconnected if it all components has cardinality $1$.

•$(X, \tau)$ is locally compact haussdoff space if $\forall X$ and $\forall U_x\in \tau$ containing $x$ there exists $V_x\in \tau$ such that $x\in \overline{V_x}\subset U_x$ where $\overline{V_x}$ is compact.

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My question:

1. Does there exists any locally compact haussdoff space $(X, \tau) $ which is totally disconnected but not zero dimensional?

2. Does there exists any locally compact haussdoff space $(X, \tau) $ which is zero dimensional but not totally disconnected?

We know a zero dimensional haussdoff space is necessarily totally disconnected. So the answer of $2$ is "no".

If the answer of $1$ is " No" , can we replace locally compact haussdoff space by a regular space to get the answer "Yes"?