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I'm reading this proof on the matter:

https://math.stackexchange.com/questions/278755/show-that-a-retract-of-a-hausdorff-space-is-closed

How do we know that the final neighborhood they come up with is disjoint from A?

https://math.stackexchange.com/questions/278755/show-that-a-retract-of-a-hausdorff-space-is-closed

How do we know that the final neighborhood they come up with is disjoint from A?

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