Write a paragraph about connected sets and their application.

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When we think of a connected set A in the plane we think that it means that between any two points x and y in A we can find a continuous path with x as beginning and y as end point, that is totally contained in A. Topologists call this property "path connected", and have another definition of connected: A is connected if we can not write A as the disjoint union of sets B and C that are disjoint and open in A....
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