An element of an algebraic closure system has this property if and only if it is finitely generated. The Arzela-Ascoli theorem gives a set of criteria for determining whether a subset of the set of continuous functions betwee
An element of an algebraic closure system has this property if and only if it is finitely generated. The Arzela-Ascoli theorem gives a set of criteria for determining whether a subset of the set of continuous functions between two metric spaces has this property, and Tychonoff's theorem states that the topological product of any number of spaces with this property will also have it.  A set is said to have this property if every open cover contains a finite subcover. For 10 points, identify this topological property that, when applied to subsets of Rn according to the Heine-Borel theorem, is equivalent to being closed and bounded.
An element of an algebraic closure system has this property if and only if it is finitely generated.
compactness