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Are closures and interiors of connected sets always connected?

Interior definition: the interior of a s et is the union of all its open subsets

Concept question: What does it mean by closures of connected sets? How are closed sets related to connected sets?

Beacon
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    If $A$ is any set in a topological space, it has a closure in that space. The question here could be paraphrased as follows: If $A$ is a connected set, are its closure and interior also connected sets? – Brian M. Scott Apr 28 '20 at 01:33
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    https://math.stackexchange.com/questions/141503/the-interior-of-a-connected-set-in-mathbb-rk https://math.stackexchange.com/questions/678032/the-closure-of-a-connected-set-in-a-topological-space-is-connected – Jake28 Apr 28 '20 at 07:57

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