A topological space that is not connected, i.e., which can be decomposed as the disjoint union of two nonempty open subsets. Equivalently, it can be characterized as a space with more than one connected component.
A subset of the Euclidean plane with more than one element can always be disconnected by cutting it through with a line (i.e., by taking out its intersection with a suitable straight line). In fact, it is certainly possible to find a line such that two points of lie on different sides of . If the Cartesian equation of is
(1)
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for fixed real numbers , then the set is disconnected, since it is the union of the two nonempty open subsets
(2)
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and
(3)
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which are the sets of elements of lying on the two sides of .