Editing Separated sets (section)

==Relation to connected spaces==
{{main|Connected space}}

Given a topological space ''X'', it is sometimes useful to consider whether it is possible for a subset ''A'' to be separated from its [[complement (set theory)|complement]]. This is certainly true if ''A'' is either the empty set or the entire space ''X'', but there may be other possibilities. A topological space ''X'' is ''connected'' if these are the only two possibilities. Conversely, if a nonempty subset ''A'' is separated from its own complement, and if the only [[subset]] of ''A'' to share this property is the empty set, then ''A'' is an ''open-connected component'' of ''X''. (In the degenerate case where ''X'' is itself the [[empty set]] <math>\emptyset</math>, authorities differ on whether <math>\emptyset</math> is connected and whether <math>\emptyset</math> is an open-connected component of itself.)