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Separated sets
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<p>In <a href="/facts/Topology/2EqW47cU">topology</a> and related branches of <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, separated sets are pairs of <a href="/facts/Subset/SJGERmbA">subsets</a> of a given <a href="/facts/Topological_space/v2ut7CbK">topological space</a> that are related to each other in a certain way: roughly speaking, neither overlapping nor touching. The notion of when two sets are separated or not is important both to the notion of <a href="/facts/Connected_space/5CUTxfoA">connected spaces</a> (and their connected components) as well as to the <a href="/facts/Separation_axiom/s4CKf8gp">separation axioms</a> for topological spaces. </p><p>Separated sets should not be confused with <a href="/facts/Separated_space/gbKIrusl">separated spaces</a> (defined below), which are somewhat related but different. <a href="/facts/Separable_space/2bmU73bk">Separable spaces</a> are again a completely different topological concept. </p>