text: In the Borel hierarchy, sets with this property correspond to the class denoted by a pi with superscript zero and subscript 1.
full_question: In the Borel hierarchy, sets with this property correspond to the class denoted by a pi with superscript zero and subscript 1. The diagonal set, defined as a subset of the product space of X with itself, has this property if and only if X is Hausdorff. A sequence of real valued continuous functions defined on a finite bounded interval with this property has a uniformly convergent subsequence, according to the Arzela-Ascoli theorem. Cantor's intersection theorem begins by considering a decreasing sequence of nonempty, bounded sets with this property. A subspace is compact if and only if it is bounded and has this property according to the Heine-Borel theorem. The Cantor set has this property because it contains only boundary points. For 10 points, name this property of sets that have an open complement.
first_sentence: In the Borel hierarchy, sets with this property correspond to the class denoted by a pi with superscript zero and subscript 1.
raw_answer: closure [or closed]