A set is not the union of two nonempty dispoint open set is called
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In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets. ... A subset of a topological space X is a connected set if it is a connected space when viewed as a subspace of X.
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disconnected
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A set is not the union of two nonempty dispoint open set is called disconnected
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