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.
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.