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Is the collapse of a totally disconnected setcompact Hausdorff space still t.d.totally disconnected?

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user473423
user473423

Is the collapse of a totally disconnected set still t.d.?

Let $S$ be a totally disconnected compact Hausdorff space and let $A\subset S$ be a closed subset. Let $S/A$ denote the space we get when collapsing $A$ to a point. Is this space still totally disconnected?