In topology, the exterior of a subset S {\displaystyle S} of a topological space X {\displaystyle X} is the union of all open sets of X {\displaystyle X} which are disjoint from S . {\displaystyle S.} It is itself an open set and is disjoint from S . {\displaystyle S.} The exterior of S {\displaystyle S} in X {\displaystyle X} is often denoted by ext X S {\displaystyle \operatorname {ext} _{X}S} or, if X {\displaystyle X} is clear from context, then possibly also by ext S {\displaystyle \operatorname {ext} S} or S e . {\displaystyle S^{\operatorname {e} }.}
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